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)=e2x and g(x)=ln4x2>y=e2x.ln4x2>y' (this is another way of writing f'(x))= e2x.8x/4x2+2e2x.ln4x2>Now sub in x=5 and simplify:e2585/4(52)+2e25*ln4(52)=0.4e10+2e10*ln100

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