Please help me , find the derivative of the following function

Question

Find the derivative of the following functions

(a). g(x) = (x + 1)²(x−3)



(b) . m(x) = 2x³ - 8x7 / 7x⁵

(c) . Q(x) = e^x ln x

(d) . f(x) = x² / cos x

Answer 1

(a). g(x) = (x + 1)²(x−3)  

 

Use the product rule; let u = (x+1)², v = (x-3); (uv)' = u'v + uv'

and u' = 2(x+1), v' = 1.  (u & v are functions of x)

 

Just plug in these expressions, and simplify...g' = (uv)'

 

(b) . m(x) = (2x³ - 8x⁷) / 7x⁵  

 

I ASSUME YOU SHOULD HAVE ENCLOSED ALL TERMS PRIOR TO /  IN PARENTHESES.

 

Why not divide the monomial into each of the numerator's terms & then do termwise differentiation.

 

(c) . Q(x) = ex ln x     Use the product rule, with u=e^x and v = ln x;  u' = e^x and v' = 1/x

 

Enough help!