What is (\partial)/(\partial x)(5y^4cos(3x)) ?

The answer to (\partial)/(\partial x)(5y^4cos(3x)) is -15y^4sin(3x)

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(\partial)/(\partial x)(5y^4cos(3x))

\frac{\partial}{\partial x} (5 y^{4} cos (3 x))

- 15 y^{4} sin (3 x)

Solution steps

\frac{\partial}{\partial x} (5 y^{4} cos (3 x))

Treat

y

as a constant

Take the constant out:

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

= 5 y^{4} \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

= 5 y^{4} (- sin (3 x) \cdot 3)

Simplify

= - 15 y^{4} sin (3 x)

\frac{d}{d x} (\frac{4 x ^{3} + 6}{x})

\int_{25}^{50} 15 d x

\frac{d}{d x} (3 e^{x} + ln (x) + tan (x))

t \to 0 lim (\frac{7}{t} - \frac{7}{t ^{2} + t})

x \to 2 lim (\frac{x ^{2}}{x - 2})

What is (\partial)/(\partial x)(5y^4cos(3x)) ?
The answer to (\partial)/(\partial x)(5y^4cos(3x)) is -15y^4sin(3x)