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

The answer to (\partial)/(\partial x)(sin(x^2*y^2)) is cos(x^2y^2)*2y^2x

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(\partial)/(\partial x)(sin(x^2*y^2))

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

cos (x^{2} y^{2}) \cdot 2 y^{2} x

Solution steps

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

Treat

y

as a constant

Apply the chain rule:

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

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

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

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

x^{2} \frac{d y}{d x} + 2 x y = ln (x)

\int \frac{3 x}{x ^{2} - 2} d x

\int (5 x^{2} + 3 x^{- 2}) d x

\frac{d y}{d x}, (cos (π x) + sin (π y))^{5} = 23

What is (\partial)/(\partial x)(sin(x^2*y^2)) ?
The answer to (\partial)/(\partial x)(sin(x^2*y^2)) is cos(x^2y^2)*2y^2x