Differentiation of Inverse Trigonometric FunctionsHere are the derivatives of inverse trigonometric functions.If y = sin-1 x, y' = 1√(1−x2)1(1−x2) If y = cos-1 x, y' = −1√(1−x2)−1(1−x2) If y = tan-1 x, y' = 1(1+x2)1(1+x2) If y = cot-1 x...
Theo. 3.17 Leibniz formula[f(x)⋅g(x)](n)=n∑k=0Cknf(k)(x)g(n−k)(x)[f(x)⋅g(x)](n)=∑k=0nCnkf(k)(x)g(n−k)(x)Proof Theo. 3.17 This clearly holds when n=1n=1. Assuming that this holds when n=tn=t. When n=t+1n=t+1, we have (t+1)={[f(x)...
FormulaPossible Generalizations#A Case: Height and Slopes#Translating into Function Language#Generalized First Inequality#Generalized Second Inequality#Rules of DifferentiationArithmetic of derivativesDerivatives of rational functions and trigonometric functionsDerivatives of composite functions and inverse functions#...
Chain Rule Formula in differentiation is defined for composite functions. Chain rule, chain rule of differentiation, chain rule formula, chain rule in differentiation, chain rule problems at BYJU'S
For instance, the expression example4′ has partial derivative:∂example4′∂x=∂y×y∂y|y=x+x×∂x+x∂x+∂y×y∂x|y=x+x=((x+x)+(x+x))×(1+1)+0 This formula (Lemma 1) is captured in a Letin type class with a method letin, which in turn is defined in ter...