What is (\partial)/(\partial x)(3y^2sin(6x)) ?

The answer to (\partial)/(\partial x)(3y^2sin(6x)) is 18y^2cos(6x)

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(\partial)/(\partial x)(3y^2sin(6x))

\frac{\partial}{\partial x} (3 y^{2} sin (6 x))

18 y^{2} cos (6 x)

Solution steps

\frac{\partial}{\partial x} (3 y^{2} sin (6 x))

Treat

y

as a constant

Take the constant out:

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

= 3 y^{2} \frac{\partial}{\partial x} (sin (6 x))

Apply the chain rule:

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

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

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

= 3 y^{2} cos (6 x) \cdot 6

Simplify

= 18 y^{2} cos (6 x)

\int 5 sin (x) d x

x y^{^{'}} - 3 y^{^{'}} - (x - 3) sin (x) + y = 0

x = \frac{1}{3} (y^{2} + 2)^{\frac{3}{2}}, 1 \leq y \leq 5

f^{^{'}} (x) = 12 x^{2} - 6 x + 1, f (1) = 5

\int \frac{5}{x ( 1 + x )} d x

What is (\partial)/(\partial x)(3y^2sin(6x)) ?
The answer to (\partial)/(\partial x)(3y^2sin(6x)) is 18y^2cos(6x)