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

The answer to (\partial)/(\partial x)(y^5cos(6x)*6) is -36y^5sin(6x)

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

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

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

Solution steps

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

Treat

y

as a constant

Take the constant out:

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

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

Apply the chain rule:

- sin (6 x) \frac{\partial}{\partial x} (6 x)

= - sin (6 x) \frac{\partial}{\partial x} (6 x)

\frac{\partial}{\partial x} (6 x) = 6

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

Simplify

= - 36 y^{5} sin (6 x)

\frac{d}{d x} (\frac{1 + ln ( x )}{1 - ln ( x )})

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

- \frac{6 x}{x ^{2} + 1}, at x = 1

f (x) = 9 x^{2}

\int \frac{x}{1 - 5 x ^{2}} d x

What is (\partial)/(\partial x)(y^5cos(6x)*6) ?
The answer to (\partial)/(\partial x)(y^5cos(6x)*6) is -36y^5sin(6x)