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

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

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

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

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

Solution steps

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

Treat

y

as a constant

Take the constant out:

(a \cdot f)^{'} = a \cdot f^{'}

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

Apply the chain rule:

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

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

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

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

\int_{2}^{\infty} e^{- 5 x} d x

\int 7 ln (x^{2} - x + 2) d x

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

\frac{d}{d x} (cos (\frac{3 x ^{2}}{x + 2}))

x \to 2 lim ([7 f (x) + g (x)])

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