What is (\partial)/(\partial x)(x^5sin(y)) ?

The answer to (\partial)/(\partial x)(x^5sin(y)) is 5x^4sin(y)

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(\partial)/(\partial x)(x^5sin(y))

\frac{\partial}{\partial x} (x^{5} sin (y))

5 x^{4} sin (y)

Solution steps

\frac{\partial}{\partial x} (x^{5} sin (y))

Treat

y

as a constant

Take the constant out:

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

= sin (y) \frac{\partial}{\partial x} (x^{5})

Apply the Power Rule:

\frac{d}{d x} (x^{a}) = a \cdot x^{a - 1}

= sin (y) \cdot 5 x^{5 - 1}

Simplify

= 5 x^{4} sin (y)

\int x cos (7 x^{2}) d x

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

\int_{0}^{1} 3 + 9 x^{2} d x

\frac{d}{d x} (\frac{e ^{x}}{9 x})

\int_{0}^{1} (2 x - 3) (5 x + 1) d x

What is (\partial)/(\partial x)(x^5sin(y)) ?
The answer to (\partial)/(\partial x)(x^5sin(y)) is 5x^4sin(y)