What is (\partial)/(\partial x)(y^4cos(5x)) ?

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

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(\partial)/(\partial x)(y^4cos(5x))

\frac{\partial}{\partial x} (y^{4} cos (5 x))

- 5 y^{4} sin (5 x)

Solution steps

\frac{\partial}{\partial x} (y^{4} cos (5 x))

Treat

y

as a constant

Take the constant out:

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

= y^{4} \frac{\partial}{\partial x} (cos (5 x))

Apply the chain rule:

- sin (5 x) \frac{\partial}{\partial x} (5 x)

= - sin (5 x) \frac{\partial}{\partial x} (5 x)

\frac{\partial}{\partial x} (5 x) = 5

= y^{4} (- sin (5 x) \cdot 5)

Simplify

= - 5 y^{4} sin (5 x)

\int_{5}^{8} \frac{1}{9 + ( x - 5 ) ^{2}} d x

n = 1 \sum \infty 2^{n + 1} - 2^{n}

n = 0 \sum \infty (sin (8))^{n}

\frac{d}{d x} (\frac{( 4 x - 2 ) ^{4}}{( - 5 x + 1 ) ^{5}})

\int (\frac{x ^{2} - 4}{x}) d x

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