How do you differentiate # f(x)=(2x+1)^(5/2) (4x-1)^(3/4) # using the product rule?

Question

1269 views around the world

You can reuse this answer
Creative Commons License

Answer 1 · 2015-10-30T15:44:24

See pointer for calculation method in Explanation

Let #u= (2x+1)^(5/2)" "# then we have #(du)/dx = 5/2(2x+1)^(3/2)(2)#

Let #v = (4x-1)^(3/4)" "# then #(dv)/dx = 3/4(4x-1)^(-1/4)(4)#

So
#(du)/dx = 5/(cancel(2))(2x+1)^(3/2)cancel((2))#

#(dv)/dx = 3/(cancel(4))(4x-1)^(-1/4)(cancel(4)) = 3/((4x-1)^(1/4))#

Substitute into:

#f^'(x) = v(du)/dx + u(dv)/dx#

Once that is done it is a matter of simplification!