Answer to Question #301559 in Calculus for HnKpehe

Question

Write an example of a function whose derivative can be found by using the following rules:

a) Product rule and special function differentiation rules

b) Power rule, quotient rule, and chain rule

c) Chain rule twice

d) Implicit differentiation and special function differentiation rule

Answer 1

Solution:

(a):

$f(x)=(2x+1)(3x-4)$

(b):

Power rule: $f(x)=x^7$

quotient rule: $f(x)=\dfrac{x+4}{4x-1}$

chain rule: $f(x)=\sin^4x$

(c):

Chain rule twice: $f(x)=\sin^4x^3$

(d):

$f(x)=y=(7x+2)^3(2x-5)^2$