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

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

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

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

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derivative of

x^{5} sin (x)

5 x^{4} sin (x) + cos (x) x^{5}

Solution steps

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

Apply the Product Rule:

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

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

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

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

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

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

x \to 0 lim (\frac{1 - cos ^{2} ( 3 x )}{x ^{2}})

f (x) = 3 arcsin (x^{4})

\int_{0}^{1} 3 x^{2} d x

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

\int 10 sinh (4 x - ln (2)) d x

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