What is implicit (dy)/(dx),y=x^2sin(8x) ?

The answer to implicit (dy)/(dx),y=x^2sin(8x) is (dy)/(dx)=2xsin(8x)+cos(8x)*8x^2

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implicit (dy)/(dx),y=x^2sin(8x)

implicit derivative

\frac{d y}{d x}, y = x^{2} sin (8 x)

\frac{d y}{d x} = 2 x sin (8 x) + cos (8 x) \cdot 8 x^{2}

Solution steps

y = x^{2} sin (8 x)

Treat

y

y (x)

Differentiate both sides:

\frac{d y}{d x} = 2 x sin (8 x) + cos (8 x) \cdot 8 x^{2}

Isolate

\frac{d y}{d x} : \frac{d y}{d x} = 2 x sin (8 x) + cos (8 x) \cdot 8 x^{2}

\frac{d y}{d x} = 2 x sin (8 x) + cos (8 x) \cdot 8 x^{2}

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\int \frac{cos ^{2} ( x )}{x ^{2}} d x

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\frac{\partial}{\partial y} (y^{3} cos (5 x))

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What is implicit (dy)/(dx),y=x^2sin(8x) ?
The answer to implicit (dy)/(dx),y=x^2sin(8x) is (dy)/(dx)=2xsin(8x)+cos(8x)*8x^2