differentiate using chain rule

Question

(x²+3x)⁷  

 

 

and 

 

√(1/x-x²⁾

 

 

 

 

Answer 1

You differentiate from the outside in.

 

(x² + 3x)⁷

 

First use the power rule, then take the derivative of the inside:

 

7(x² + 3x)^7-1 d/dx (x² + 3x)

 

7(x² + 3x)⁶ * (2x+3)

 

 

 I'm going to rewrite the second problem:

 

(1/x + x²)^1/2

 

Again, use the power rule, then take the derivative of the inside:

 

(1/2)*(1/x + x²)^-1/2 * d/dx (1/x + x²)

 

(1/2)*(1/x + x²)^-1/2 * (ln x + 2x)