What is (\partial)/(\partial x)(x^4sin(2t)) ?

The answer to (\partial)/(\partial x)(x^4sin(2t)) is 4x^3sin(2t)

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(\partial)/(\partial x)(x^4sin(2t))

\frac{\partial}{\partial x} (x^{4} sin (2 t))

4 x^{3} sin (2 t)

Solution steps

\frac{\partial}{\partial x} (x^{4} sin (2 t))

Treat

t

as a constant

Take the constant out:

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

= sin (2 t) \frac{\partial}{\partial x} (x^{4})

Apply the Power Rule:

\frac{d}{d x} (x^{a}) = a \cdot x^{a - 1}

= sin (2 t) \cdot 4 x^{4 - 1}

Simplify

= 4 x^{3} sin (2 t)

sin (x) + \frac{4}{3} cot (x)

\int \frac{1}{x ^{2} - 7 x + 12} d x

x y^{2} \frac{d y}{d x} = y^{3} - 3 x^{3}, y (1) = 5

y^{^{'}} = 0.1 \cdot y - 250000

f (x) = 3 cos^{2} (x)

What is (\partial)/(\partial x)(x^4sin(2t)) ?
The answer to (\partial)/(\partial x)(x^4sin(2t)) is 4x^3sin(2t)