What is the derivative of (3(x^2+2^3)/5) ?

The derivative of (3(x^2+2^3)/5) is (18x(x^2+2)^2)/5

What is the first derivative of (3(x^2+2^3)/5) ?

The first derivative of (3(x^2+2^3)/5) is (18x(x^2+2)^2)/5

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\frac{d}{d x} (\frac{3 ( x ^{2} + 2 ) ^{3}}{5})

\frac{18 x ( x ^{2} + 2 ) ^{2}}{5}

Solution steps

\frac{d}{d x} (\frac{3 ( x ^{2} + 2 ) ^{3}}{5})

Take the constant out:

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

= \frac{3}{5} \frac{d}{d x} ((x^{2} + 2)^{3})

Apply the chain rule:

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

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

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

= \frac{3}{5} \cdot 3 (x^{2} + 2)^{2} \cdot 2 x

Simplify

\frac{3}{5} \cdot 3 (x^{2} + 2)^{2} \cdot 2 x : \frac{18 x ( x ^{2} + 2 ) ^{2}}{5}

= \frac{18 x ( x ^{2} + 2 ) ^{2}}{5}

\frac{d x}{d t} = a x

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

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

\frac{\partial}{\partial a} (a x)

\frac{1}{s \cdot ( s + 5 ) ^{2}}

What is the derivative of (3(x^2+2^3)/5) ?
The derivative of (3(x^2+2^3)/5) is (18x(x^2+2)^2)/5
What is the first derivative of (3(x^2+2^3)/5) ?
The first derivative of (3(x^2+2^3)/5) is (18x(x^2+2)^2)/5