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

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

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

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

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

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

Solution steps

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

Take the constant out:

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

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

Apply the chain rule:

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

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

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

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

Simplify

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

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

\int_{1}^{5} \frac{4}{x ^{2}} d x

\frac{d}{d y} (arctan (y))

\int tan (g) (x) d x

\int cosh (t) d t

\frac{x + 5}{x + 1}

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