What is the derivative of 1/3 sqrt((16+x^2^3)) ?

The derivative of 1/3 sqrt((16+x^2^3)) is xsqrt(x^2+16)

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

The first derivative of 1/3 sqrt((16+x^2^3)) is xsqrt(x^2+16)

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

x x^{2} + 16

Solution steps

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

Take the constant out:

(a \cdot f)^{'} = a \cdot f^{'}

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

Apply the chain rule:

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

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

\frac{d}{d x} ((16 + x^{2})^{3}) = 6 x (16 + x^{2})^{2}

= \frac{1}{3} \cdot \frac{1}{2 ( 16 + x ^{2} ) ^{3}} \cdot 6 x (16 + x^{2})^{2}

Simplify

\frac{1}{3} \cdot \frac{1}{2 ( 16 + x ^{2} ) ^{3}} \cdot 6 x (16 + x^{2})^{2} : x x^{2} + 16

= x x^{2} + 16

\int \frac{1}{4 x ^{2} - 7} d x

\int_{0}^{t} 9 e^{s} sin (t - s) d s

f (x) = (2 - x) e^{x}

x \to 0 + lim (2)

t

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