[Maths Class Notes] on Differentiation Formula Pdf for Exam

Differentiation is defined as the rate of change of a quantity with respect to another. For example, speed is measured as the rate of change of distance with respect to time. It also helps us to determine the rate of change of variable x with respect to y. The graph of y drawn against x is the gradient of the curve. 

This formula list consists of derivatives for constant, trigonometric functions, polynomials, hyperbolic, logarithmic functions, exponential, inverse trigonometric functions, etc. 

Differentiation Formulas List

In all the formulas below, f’ means d(f(x))/dx = f′(x) and g’ means d(g(x))/dx = g′(x) . Both f are the functions of x and and g is differentiated with respect to x. We can also represent dy/dx = Dx/y. Some of the general differentiation formulas are;

Power Rule: [ (d/dx) (x^{n}) = nx(^{n – 1})]

Derivative of a constant, a:  (d/dx) (a) = 0

Derivative of a constant multiplied with function f: (d/dx) (a. f) = af’

Sum Rule: (d/dx) (f ± g) = f’ ± g’

Product Rule: (d/dx) (fg)= fg’ + gf’ 

Quotient Rule: d/dx(fg) = gf′–fg′g[_{2}]

Differentiation Formulas for Trigonometric Functions

• d/dx (sin x) = cosx

• d/dx (cos x) = –sinx

• d/dx (tan x) = sec 2x

• d/dx (cot x) = −cosec 2x

• d/dx (sec x) = sec x tan x

• d/dx (cosec x) =−cosec x cot x

• d/dx(sinh x) =cosh x

• d/dx(cosh x) =sinh x

• d//dx(tanh x) =sec h 2x

• d/dx(coth x) =−cosech 2x

• d/dx(sech x) =−sech x tanh x

• ddx(cosech x) =−cosec h x coth x

Differentiation Formulas for

If y = sin-1 x, y’ = [1 sqrt{(1-x^{2})}]

If y = cos-1 x, y’ = [-1 sqrt{(1-x^{2})}]

If y = tan-1 x, y’ = [1(1+x^{2})]

If y = cot-1 x, y’ =[−1(1+x^{2})]

If y = sec-1 x, y’ = [1x sqrt{(x^{2}−1)}]

If y = cosec-1 x, y’ = [−1xsqrt{(x^{2}−1)}]