All Differentiation Formulas PDF Summary
Dear readers, here we are offering Differentiation Formulas PDF to all of you. The differentiation formulas are those which help in solving all problems related to differentiation and its equations which may include derivatives of trigonometric functions, logarithmic functions to basic functions.
Differentiation is very important for the students and for those who are preparing for either any government examination or a competitive examination. It lays the concrete foundation for the vast and advanced concepts of calculus. This concept not only helps the students to score high marks in maths but also in physics and chemistry as well.
Differentiation Formulas PDF
- Power Rule: (d/dx) (xn ) = 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:ddx(fg) d d x ( f g ) = gf′–fg′g2.
Differentiation Formulas for Trigonometric Functions
Trigonometry is the concept of the relationship between angles and sides of triangles. Here, we have 6 main ratios, such as, sine, cosine, tangent, cotangent, secant, and cosecant. You must have learned about basic trigonometric formulas based on these ratios. Now let us see, the formulas for derivatives of trigonometric functions.
- (frac{d}{dx} (sin~ x)= cos x)
- (frac{d}{dx} (cos~ x)= – sin x)
- (frac{d}{dx} (tan ~x)= sec^{2} x)
- (frac{d}{dx} (cot~ x = -cosec^{2} x)
- (frac{d}{dx} (sec~ x) = sec x tan x)
- (frac{d}{dx} (cosec ~x)= -cosec x cot x)
- (frac{d}{dx} (sinh~ x)= cosh x)
- (frac{d}{dx} (cosh~ x) = sinh x)
- (frac{d}{dx} (tanh ~x)= sech^{2} x)
- (frac{d}{dx} (coth~ x)=-cosech^{2} x)
- (frac{d}{dx} (sech~ x)= -sech x tanh x)
- (frac{d}{dx} (cosech~ x ) = -cosech x coth x)
Differentiation Formulas for Inverse Trigonometric Functions
Inverse trigonometry functions are the inverse of trigonemetric ratios. Let us see the formulas for derivative of inverse trigonometric functions.
- (frac{d}{dx}(sin^{-1}~ x)) = (frac{1}{sqrt{1 – x^2}})
- (frac{d}{dx}(cos^{-1}~ x)) = (-frac{1}{sqrt{1 – x^2}})
- (frac{d}{dx}(tan^{-1}~ x)) = (frac{1}{1 + x^2})
- (frac{d}{dx}(cot^{-1}~ x)) = (-frac{1}{1 + x^2})
- (frac{d}{dx}(sec^{-1} ~x) )= (frac{1}{|x|sqrt{x^2 – 1}})
- (frac{d}{dx}(cosec^{-1}~x) )= (-frac{1}{|x|sqrt{x^2 – 1}})
Other Differentiation Formulas
- (frac{d}{dx}(a^{x}) = a^{x} ln a)
- (frac{d}{dx}(e^{x}) = e^{x})
- (frac{d}{dx}(log_a~ x)) = (frac{1}{(ln~ a)x})
- (frac{d}{dx}(ln~ x) = 1/x)
- Chain Rule: (frac{dy}{dx}) = (frac{dy}{du} × frac{du}{dx}) = (frac{dy}{dv} × frac{dv}{du} × frac{du}{dx})
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