What is (\partial)/(\partial x)(5y^6cos(5x)) ?

The answer to (\partial)/(\partial x)(5y^6cos(5x)) is -25y^6sin(5x)

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(\partial)/(\partial x)(5y^6cos(5x))

\frac{\partial}{\partial x} (5 y^{6} cos (5 x))

- 25 y^{6} sin (5 x)

Solution steps

\frac{\partial}{\partial x} (5 y^{6} cos (5 x))

Treat

y

as a constant

Take the constant out:

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

= 5 y^{6} \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

= 5 y^{6} (- sin (5 x) \cdot 5)

Simplify

= - 25 y^{6} sin (5 x)

f (x) = \frac{6 - x ^{2}}{6 + x ^{2}}

\frac{d ^{3}}{d x ^{3}} (ln (1 + x))

k = 1 \sum \infty \frac{k}{e ^{7 k}}

\frac{( e ^{- s} )}{s}

\frac{\partial}{\partial x} (9 x sin (4 x^{2} y))

What is (\partial)/(\partial x)(5y^6cos(5x)) ?
The answer to (\partial)/(\partial x)(5y^6cos(5x)) is -25y^6sin(5x)