Answer
$f(x)=(4x^2-25)(20-7 \ln x)$
$f^{'}(x)=(20-7 \ln x) [ 8x]+ (4x^2-25)[ - (\frac{7}{x}])$
Work Step by Step
$g(x)=4x^2-25$
$h(x)=20-7 \ln x$
(a)
Let
$f(x)=g(x)h(x)$
$\Longrightarrow$
$f(x)=(4x^2-25)(20-7 \ln x)$
(b)
Taking derivative of f(x) with respect to x
$f^{'}(x)=(20-7 \ln x)\frac{d (4x^2-25)}{dx}+ (4x^2-25)\frac{d(20-7 \ln x)}{dx}$
$f^{'}(x)=(20-7 \ln x) [ \frac{d(4x^2)}{dx}- \frac{d(25)}{dx}]+ (4x^2-25)[ \frac{d(20)}{dx}-\frac{d(7 \ln x)}{dx}]$
$f^{'}(x)=(20-7 \ln x) [ 4\frac{d(x^2)}{dx}-0]+ (4x^2-25)[ 0-7\frac{d( \ln x)}{dx}]$
$f^{'}(x)=(20-7 \ln x) [ 4(2x)]+ (4x^2-25)[ -7 (\frac{1}{x}])$
$f^{'}(x)=(20-7 \ln x) [ 8x]+ (4x^2-25)[ - (\frac{7}{x}])$
