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White raven [17]
4 years ago
13

Find the dy/dx for the equation below using implicit differentiation.

Mathematics
1 answer:
n200080 [17]4 years ago
6 0

First of all, recall that y is a product of function of x. We have three factors:

f(x)=x^2,\quad g(x)=e^{3x},\quad h(x)=\sin(4x)

The derivative of a product of function is computed by deriving one function at the time, and then adding all the results:

y' = f'(x)g(x)h(x)+f(x)g'(x)h(x)+f(x)g(x)h'(x)

Let's compute the derivative of each function first:

f'(x)=2x,\quad g'(x) = 3e^{3x},\quad h'(x)=4\cos(4x)

Now plug f, f', g, g', h, h' in the formula above as required:

2xe^{3x}\sin(4x)+3x^2e^{3x}\sin(4x)+4x^2e^{3x}\cos(4x)

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