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

The answer to (\partial)/(\partial x)(x^4sin(2x)) is 4x^3sin(2x)+cos(2x)*2x^4

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

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

4 x^{3} sin (2 x) + cos (2 x) \cdot 2 x^{4}

Solution steps

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

Apply the Product Rule:

(f \cdot g)^{'} = f^{'} \cdot g + f \cdot g^{'}

f = x^{4}, g = sin (2 x)

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

\frac{\partial}{\partial x} (x^{4}) = 4 x^{3}

\frac{\partial}{\partial x} (sin (2 x)) = cos (2 x) \cdot 2

= 4 x^{3} sin (2 x) + cos (2 x) \cdot 2 x^{4}

e^{- (t - 1)}

\frac{d}{d x} (x - ln (sec (x) + tan (x)))

(- 2 x^{3} + x^{2} - 2 x - 1) x^{3}

\frac{d}{d x} (2 e^{5 x})

\int 2 x y + 2 x d x

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