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Popular >

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

Solution

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

Solution

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

Solution steps

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

Treat

y

as a constant

Take the constant out:

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

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

Simplify

= - 9 y^{4} sin (3 x)

Popular Examples

integral of (8x^3)/(x-5)

\int \frac{8 x ^{3}}{x - 5} d x

limit as x approaches 0 of ((x+2)^2-4)/x

x \to 0 lim (\frac{( x + 2 ) ^{2} - 4}{x})

f (x) = x e^{x} - e^{x}

integral of 7e^6

\int 7 e^{6} d x

limit as t approaches 1 of 1/(t-1)

t \to 1 lim (\frac{1}{t - 1})

Frequently Asked Questions (FAQ)

What is (\partial)/(\partial x)(y^4cos(3x)*3) ?
The answer to (\partial)/(\partial x)(y^4cos(3x)*3) is -9y^4sin(3x)