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}

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Popular >

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

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}}

\frac{d}{d x} (\frac{3 x ^{4}}{tan ( x )})

5^{2 x}

\frac{d}{d x} (\frac{q x + r}{s x + r})

x \to 0 + lim (\frac{- ln ( 1 + 6 x )}{x})

3 x

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}