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

The answer to (\partial)/(\partial x)(y^4cos(5x)*5) is -25y^4sin(5x)

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

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

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

Solution steps

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

Treat

y

as a constant

Take the constant out:

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

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

Simplify

= - 25 y^{4} sin (5 x)

\int_{0}^{\frac{5}{8}} \frac{1}{( 64 x ^{2} + 1 ) ^{\frac{3}{2}}} d x

\frac{d y}{d x} = \frac{3 e ^{x}}{y ^{2}}

e^{- t} \cdot (cos (4 t) - 2 sin (4 t))

n = 3 \sum \infty \frac{1}{n ^{2}}

F (x) = 5 x^{5} (x^{3} - 9 x)

What is (\partial)/(\partial x)(y^4cos(5x)*5) ?
The answer to (\partial)/(\partial x)(y^4cos(5x)*5) is -25y^4sin(5x)