Find the gradient of the equation y=e^2x.ln(4x^2) when x=5.

>First know that you must differentiate to find the gradient. To differentiate this function you must use the product rule which is:>d/dx(f(x)g(x))=f(x)g'(x)+f'(x)g(x)>Now apply this rule to the formula where f(x)=e^2x and g(x)=ln4x²>y=e^2x.ln4x²>y' (this is another way of writing f'(x))= e^2x.8x/4x²+2e^2x.ln4x²>Now sub in x=5 and simplify:e²⁵85/4(5²)+2e²5*ln4(5²)=0.4e¹⁰+2e¹⁰*ln100