What is (\partial)/(\partial x)(3y^2sin(3x)) ?

The answer to (\partial)/(\partial x)(3y^2sin(3x)) is 9y^2cos(3x)

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(\partial)/(\partial x)(3y^2sin(3x))

\frac{\partial}{\partial x} (3 y^{2} sin (3 x))

9 y^{2} cos (3 x)

Solution steps

\frac{\partial}{\partial x} (3 y^{2} sin (3 x))

Treat

y

as a constant

Take the constant out:

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

= 3 y^{2} \frac{\partial}{\partial x} (sin (3 x))

Apply the chain rule:

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

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

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

= 3 y^{2} cos (3 x) \cdot 3

Simplify

= 9 y^{2} cos (3 x)

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

\int - 36 sin (6 t - \frac{π}{2}) d t

\int_{0}^{1} \frac{1}{1 + x} d x

2 9 + x^{2}

\int_{0}^{2 π} sin (x) d x

What is (\partial)/(\partial x)(3y^2sin(3x)) ?
The answer to (\partial)/(\partial x)(3y^2sin(3x)) is 9y^2cos(3x)