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Popular >

derivative of x^2(x+sin(x)^5)

Solution

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

Solution

2 x (x + sin (x))^{5} + 5 (x + sin (x))^{4} (1 + cos (x)) x^{2}

Solution steps

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

Apply the Product Rule:

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

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

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

\frac{d}{d x} (x^{2}) = 2 x

\frac{d}{d x} ((x + sin (x))^{5}) = 5 (x + sin (x))^{4} (1 + cos (x))

= 2 x (x + sin (x))^{5} + 5 (x + sin (x))^{4} (1 + cos (x)) x^{2}

Graph

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Frequently Asked Questions (FAQ)

What is the derivative of x^2(x+sin(x)^5) ?
The derivative of x^2(x+sin(x)^5) is 2x(x+sin(x))^5+5(x+sin(x))^4(1+cos(x))x^2
What is the first derivative of x^2(x+sin(x)^5) ?
The first derivative of x^2(x+sin(x)^5) is 2x(x+sin(x))^5+5(x+sin(x))^4(1+cos(x))x^2