What is the derivative of x^5sin(2x) ?

The derivative of x^5sin(2x) is 5x^4sin(2x)+cos(2x)*2x^5

What is the first derivative of x^5sin(2x) ?

The first derivative of x^5sin(2x) is 5x^4sin(2x)+cos(2x)*2x^5

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

5 x^{4} sin (2 x) + cos (2 x) \cdot 2 x^{5}

Solution steps

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

Apply the Product Rule:

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

f = x^{5}, g = sin (2 x)

= \frac{d}{d x} (x^{5}) sin (2 x) + \frac{d}{d x} (sin (2 x)) x^{5}

\frac{d}{d x} (x^{5}) = 5 x^{4}

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

= 5 x^{4} sin (2 x) + cos (2 x) \cdot 2 x^{5}

\frac{d}{d x} (\frac{x ^{2} ( x + 1 ) ^{2}}{x - 1})

6 4 x^{2} + 5

\frac{d}{d x} (e^{y - l n (x)})

\frac{d}{d x} (\frac{x ^{4}}{x ^{5} + 3})

\frac{\partial}{\partial y} (3 x + y)

What is the derivative of x^5sin(2x) ?
The derivative of x^5sin(2x) is 5x^4sin(2x)+cos(2x)*2x^5
What is the first derivative of x^5sin(2x) ?
The first derivative of x^5sin(2x) is 5x^4sin(2x)+cos(2x)*2x^5