What is (\partial)/(\partial x)(y^6cos(3x)) ?

The answer to (\partial)/(\partial x)(y^6cos(3x)) is -3y^6sin(3x)

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(\partial)/(\partial x)(y^6cos(3x))

\frac{\partial}{\partial x} (y^{6} cos (3 x))

- 3 y^{6} sin (3 x)

Solution steps

\frac{\partial}{\partial x} (y^{6} cos (3 x))

Treat

y

as a constant

Take the constant out:

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

= y^{6} \frac{\partial}{\partial x} (cos (3 x))

Apply the chain rule:

- sin (3 x) \frac{\partial}{\partial x} (3 x)

= - sin (3 x) \frac{\partial}{\partial x} (3 x)

\frac{\partial}{\partial x} (3 x) = 3

= y^{6} (- sin (3 x) \cdot 3)

Simplify

= - 3 y^{6} sin (3 x)

\int \frac{x ^{3}}{3 ( 1 + x ^{2} )} d x

f (x) = 3 x^{2} - 4 x, at x = - 1

\frac{d}{d y} (x - 2 y)

\frac{s + 2}{( s + 1 ) ^{2}}

f (x) = 5 x^{9} x^{6}, at x = 2

What is (\partial)/(\partial x)(y^6cos(3x)) ?
The answer to (\partial)/(\partial x)(y^6cos(3x)) is -3y^6sin(3x)