What is (\partial)/(\partial x)(sin(x*y*e^{x^2})) ?

The answer to (\partial)/(\partial x)(sin(x*y*e^{x^2})) is cos(xye^{x^2})y(e^{x^2}+2e^{x^2}x^2)

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(\partial)/(\partial x)(sin(xye^{x^2}))

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

cos (x y e^{x^{2}}) y (e^{x^{2}} + 2 e^{x^{2}} x^{2})

Solution steps

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

Treat

y

as a constant

Apply the chain rule:

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

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

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

= cos (x y e^{x^{2}}) y (e^{x^{2}} + 2 e^{x^{2}} x^{2})

What is (\partial)/(\partial x)(sin(x*y*e^{x^2})) ?
The answer to (\partial)/(\partial x)(sin(x*y*e^{x^2})) is cos(xye^{x^2})y(e^{x^2}+2e^{x^2}x^2)