What is (\partial)/(\partial x)(sin^2(x^3e^y)) ?

The answer to (\partial)/(\partial x)(sin^2(x^3e^y)) is 6e^yx^2sin(e^yx^3)cos(e^yx^3)

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(\partial)/(\partial x)(sin^2(x^3e^y))

\frac{\partial}{\partial x} (sin^{2} (x^{3} e^{y}))

6 e^{y} x^{2} sin (e^{y} x^{3}) cos (e^{y} x^{3})

Solution steps

\frac{\partial}{\partial x} (sin^{2} (x^{3} e^{y}))

Treat

y

as a constant

Apply the chain rule:

2 sin (x^{3} e^{y}) \frac{\partial}{\partial x} (sin (x^{3} e^{y}))

= 2 sin (x^{3} e^{y}) \frac{\partial}{\partial x} (sin (x^{3} e^{y}))

\frac{\partial}{\partial x} (sin (x^{3} e^{y})) = cos (x^{3} e^{y}) \cdot 3 e^{y} x^{2}

= 2 sin (x^{3} e^{y}) cos (x^{3} e^{y}) \cdot 3 e^{y} x^{2}

Simplify

= 6 e^{y} x^{2} sin (e^{y} x^{3}) cos (e^{y} x^{3})

\int \frac{1}{81 e ^{- 8 x} + e ^{8 x}} d x

\frac{d}{d x} (cos (sin (2 x + 5)))

\frac{d}{d x} (\frac{a x}{b})

What is (\partial)/(\partial x)(sin^2(x^3e^y)) ?
The answer to (\partial)/(\partial x)(sin^2(x^3e^y)) is 6e^yx^2sin(e^yx^3)cos(e^yx^3)