Question

Logarithmic differentiation

f(x)=(2x-1)^-2 (x+3)^4 at x=1

f'(x)= -2*2/2x+1 + 4*1/x+3 [(2x-1)^-2)(x+3)^4 and then I plug in 1.

I am having trouble getting an answer when I plug in 1.

Answer 1

Can you re-write I think there is something missing.

Answer 2

You lost me totally

d/dx (a * b) = a db/dx + b da/dx

f= (2x-1)^-2 * (x+3)^4

f' = [(2x-1)^-2][4(x+3)^3]
+ (x+3)^4 (-2(2x-1)^-3 (2)]

at x = 1
f' = [(2-1)^-2][4(4)^3]
+ (4)^4 (-2(1)^-3 (2)]
which is
f' = [1][4^4]
+ (4)^4 (1/4]
or
4^4+4^3 = 4^3(5)= 320
check my arithmetic !