What is the derivative of xsqrt(h(x)) ?

The derivative of xsqrt(h(x)) is (3sqrt(x)sqrt(h))/2

What is the first derivative of xsqrt(h(x)) ?

The first derivative of xsqrt(h(x)) is (3sqrt(x)sqrt(h))/2

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derivative of

x h (x)

\frac{3 x h}{2}

Solution steps

\frac{d}{d x} (x h x)

Simplify

x h x : x^{\frac{3}{2}} h

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

Treat

h

as a constant

Take the constant out:

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

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

Apply the Power Rule:

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

= h \frac{3}{2} x^{\frac{3}{2} - 1}

Simplify

h \frac{3}{2} x^{\frac{3}{2} - 1} : \frac{3 x h}{2}

= \frac{3 x h}{2}

What is the derivative of xsqrt(h(x)) ?
The derivative of xsqrt(h(x)) is (3sqrt(x)sqrt(h))/2
What is the first derivative of xsqrt(h(x)) ?
The first derivative of xsqrt(h(x)) is (3sqrt(x)sqrt(h))/2