What is the derivative of h(x)=4sqrt(x^7) ?

The derivative of h(x)=4sqrt(x^7) is 14x^{5/2}

What is the first derivative of h(x)=4sqrt(x^7) ?

The first derivative of h(x)=4sqrt(x^7) is 14x^{5/2}

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derivative of

h (x) = 4 x^{7}

14 x^{\frac{5}{2}}

Solution steps

\frac{d}{d x} (4 x^{7})

Take the constant out:

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

= 4 \frac{d}{d x} (x^{7})

Apply radical rule:

= 4 \frac{d}{d x} (x^{\frac{7}{2}})

Apply the Power Rule:

\frac{d}{d x} (x^{a}) = a \cdot x^{a - 1}

= 4 \cdot \frac{7}{2} x^{\frac{7}{2} - 1}

Simplify

4 \cdot \frac{7}{2} x^{\frac{7}{2} - 1} : 14 x^{\frac{5}{2}}

= 14 x^{\frac{5}{2}}

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What is the derivative of h(x)=4sqrt(x^7) ?
The derivative of h(x)=4sqrt(x^7) is 14x^{5/2}
What is the first derivative of h(x)=4sqrt(x^7) ?
The first derivative of h(x)=4sqrt(x^7) is 14x^{5/2}