“Learn about differentiation in calculus, a fundamental concept that explores how functions change, calculating the rate of change or slope at any given point.”
Mathematics Chapter 2 Class 12
Derivative of ?x (cos x) w.r.t x is: Cos x /2?x -?xSin x
If y = eax, then y4=: a4eax
dy/dx = dy/dx . dx/du is called: Chain rule
If y=Cot hx then dy/dx=: #NAME?
d/dx cos hx =: sin hx
The Notation dy/dx is used for the derivative by: Leibniz
If c?Dfand f'(c)=0, then the number c is called a: Critical value
If y=Cos x then dy/dx=: #NAME?
If f(x)=c3 then f'(x)=: 0
If f(x) is differentiable in the neighborhood of c, where of c, where ? ‘(c) = then ? has relative minima at x = c if: f”(c) > 0
lim ?(x) – ?(a) /x-a equals: ?
If f(x)=1/x2 then f'(-1)=: 2
If y=cf(x) then dy/dx =: cf'(x)
If c?Dfand f'(c)=0, then the point (c,f(c)) on the graph of f is named as a: Critical point
The notation f'(x) is used for derivative by: Lagrange
y=Cosec hx then dy/dx=: #NAME?
If ?'(c) = 0, then f has relative maxima at x=c if: ?”(c) < 0
If f(x) = sin x, then f’ (0) =: 1
d/dx (f(x) . g(x)) =: f'(x) g(x) + f(x)g'(x)
d/dx (af(x)) =: a?(x) ? (x)Ina
d/dx (logn)=: 1/xlna
The symbol for the derivative of y with respect to x is: dy/dx
If y=x4+2x2+2, then dy/dx=: 4x?(y-1)
If y=Sin x then dy/dx=: Cos x
If y=tan x then dy/dx= Sec2 x
If y=Cot x then dy/dx=: -Cosec2 x
Y=Sec hx then dy/dx=: #NAME?
a0+a1x+a2x2+a3x3+a4x4+……………..+anxn+ ………….. is called a: Power series
For stationary point for a function f we have f'(x)=: 0
If f(x)=x2/3 then f'(8)=: 1/3
For a function f(x), if f'(c) = 0 & f”(c) > 0 then f(x) has, at x = c: relative minima
The minimum value of the function f(x)=x2-x-2 is: -2.25
If y=eax then dy/dx =: aeax
IF f(x) = cosx then f’ (Sin-1 x)=: -x/?a-x2
d/dx asinx =: asinx cosx lna
The process of finding f’ is called: Differentiation
The notation df/dx is used for derivative by: Leibniz
If y=ax then dy/dx =: ax ln a
If f(x)=c then f'(x)=: 0
If y= Tanhx then dy/dx=: Sec h2 x
d/dx (tan-1x+ cot-1x) =: 0
The function f(x) = ax2 + bx + c has maximum value if: a<0
The notation f: Newton
d/dx[axm+bxn]: amxm-1+bnxn-1
For x1,x2? (a,b) fis increasing on the interval (a,b) for x2 > x1 if: f(x2)<f(x1)
If f(x)=1/x2 then f'(-1)=: 2
If f(x) = 1/x2, then = f'(-1) =: 2
If y=Cos x then dy/dx=: #NAME?
If y=Cosec x then dy/dx=: -Cosecx Cotx
If y = Sinx then: y2 = y
y=in(f(x)) then dy/dx=: f'(x)/f(x)
If y=af(x) then dy/dx =: f'(x)af(x) lna
If f(x)=2x2+1 then f'(-1)=: -4
Derivative of y = (x + 1)(?x + 1) is: dy/dx = (x +1) 1/2?x +(?x +1)
The Newton df(x) is used for derivative by: Caunchy
If y = e10x then y5 =: 100000e10x
If f(x) = cos x, then slope of normal at x = 0 is: undefined
d/dx ax=: axlna
If f(x) = tanx, then f'(x) =: sec2x
Derivative of log x is: 1/x/1/Ina
If y = cos-1 (x/a) then y1 =: -1/?a2 -x2
Derivative of ?tan x is: 1/2 sec2x/?tanx
Tailor Series Expansion is only valid if it is: Convergent
If y=Sinhx then dy/dx=: Coshx
If y=Sec x then dy/dx=: Sec x Tanx
The branch of calculus which mainly deals with the rate of change of a dependent variable with respect to one or more independent variables is called: Differential calculus
y=ln x: 1/x
If f(x) = x2then f'(x) =: 2x
If y= Coshx then dy/dx=: Sinhx
If y=ex then dy/dx =: ex
f(x)=xn, n: nxn-1
d/dx cosec hx =: #NAME?
Derivative of esinx is: e Sinix Cosx
Any point where f is neither increasing nor decreasing is called a: Stationary point
Derivative of the function y = |x| at x = 0: does not exist
For a square of side x units, the rate of change of area with respect to the side is given by: 2x
For any set X, a function 1 : X: An identity function
The domain of a rational function R(x)=P(x)/Q(x) is a set of all real numbers x for which: Q(x)
cos h2x + sin h2x =: cos h2x
The function of the form x=at2 & y=at are called parametric function’s and the variable t is called: Parameter
d/dx sin x3is equal to: 3x2cos x3
If f(x) = 2x + 1, then f of (x) is equal to: 4x + 3
If (x) = |x| then range of ? is: [0,?]
Polynomial function P(x) has the domain: Subset of real numbers
If (x – 2, 0) = (1, 0), then x =: 3
If y is easily expressed in terms of the independent variable x, then y is called a/an _____________ function of x: Explicit
If a function f(x) is not continuous at x = c, then it is called ————-at c: Discontinuous
If f : X: Range of f
If f(x)=x2 +1 then domain of f is: Set of all real numbers
x = a cost t, y = a sin t are parametric equations of: Circle
f(x) = x2/3is a/an: Even function
If y = f(x), then the variable x is called _________ variable of a function f: Independent
Equals x = 3 cos t, y = 3 sin t represent equation: Circle
if f(x) = 2x+3 and g(x) = x2 the fog (x) =: 2x2 + 3
If (x – 2, 0) = (1, 0) then x =: 3
If f(x)=x2 then the domain of f is: Set of all real numbers
Symbolically Explicit function can be written as: y=f(x)
The perimeter P of square as a function of its area A is: P=4?A
The function f(x) = cos x + sin x is: Neither even nor odd
f(x) = cos x + sin x is ____________ function: Nor the even nor odd
Important : Review all previous years’ 12 Class Past Papers for comprehensive practice and better exam preparation.