What is (\partial)/(\partial x)(3y^2cos(5x)) ?

The answer to (\partial)/(\partial x)(3y^2cos(5x)) is -15y^2sin(5x)

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(\partial)/(\partial x)(3y^2cos(5x))

\frac{\partial}{\partial x} (3 y^{2} cos (5 x))

- 15 y^{2} sin (5 x)

Solution steps

\frac{\partial}{\partial x} (3 y^{2} cos (5 x))

Treat

y

as a constant

Take the constant out:

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

= 3 y^{2} \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

= 3 y^{2} (- sin (5 x) \cdot 5)

Simplify

= - 15 y^{2} sin (5 x)

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

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

\frac{\partial}{\partial y} (2 arctan (\frac{y}{x}))

f (x) = 2 + 3 x - 5 x^{2}, at x = 1

h \to 1 lim (4 h^{2} + x + 3)

What is (\partial)/(\partial x)(3y^2cos(5x)) ?
The answer to (\partial)/(\partial x)(3y^2cos(5x)) is -15y^2sin(5x)