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Popular >

derivative of 1/3 (16+x^2)^{3/2}+16/3

Solution

derivative of

\frac{1}{3} (16 + x^{2})^{\frac{3}{2}} + \frac{16}{3}

Solution

x (x^{2} + 16)^{\frac{1}{2}}

Solution steps

\frac{d}{d x} (\frac{1}{3} (16 + x^{2})^{\frac{3}{2}} + \frac{16}{3})

Apply the Sum/Difference Rule:

(f \pm g)^{'} = f^{'} \pm g^{'}

= \frac{d}{d x} (\frac{1}{3} (16 + x^{2})^{\frac{3}{2}}) + \frac{d}{d x} (\frac{16}{3})

\frac{d}{d x} (\frac{1}{3} (16 + x^{2})^{\frac{3}{2}}) = x (16 + x^{2})^{\frac{1}{2}}

\frac{d}{d x} (\frac{16}{3}) = 0

= x (16 + x^{2})^{\frac{1}{2}} + 0

Simplify

= x (x^{2} + 16)^{\frac{1}{2}}

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Frequently Asked Questions (FAQ)

What is the derivative of 1/3 (16+x^2)^{3/2}+16/3 ?
The derivative of 1/3 (16+x^2)^{3/2}+16/3 is x(x^2+16)^{1/2}
What is the first derivative of 1/3 (16+x^2)^{3/2}+16/3 ?
The first derivative of 1/3 (16+x^2)^{3/2}+16/3 is x(x^2+16)^{1/2}