What is the derivative of xsqrt(x)+x^2sqrt(x) ?

The derivative of xsqrt(x)+x^2sqrt(x) is (3sqrt(x)+5x^{3/2})/2

What is the first derivative of xsqrt(x)+x^2sqrt(x) ?

The first derivative of xsqrt(x)+x^2sqrt(x) is (3sqrt(x)+5x^{3/2})/2

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

\frac{3 x + 5 x ^{\frac{3}{2}}}{2}

Solution steps

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

Simplify

x x + x^{2} x : x^{\frac{3}{2}} + x^{\frac{5}{2}}

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

Apply the Sum/Difference Rule:

(f \pm g)^{'} = f^{'} \pm g^{'}

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

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

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

= \frac{3 x}{2} + \frac{5 x ^{\frac{3}{2}}}{2}

Apply rule

\frac{a}{c} \pm \frac{b}{c} = \frac{a \pm b}{c}

= \frac{3 x + 5 x ^{\frac{3}{2}}}{2}

What is the derivative of xsqrt(x)+x^2sqrt(x) ?
The derivative of xsqrt(x)+x^2sqrt(x) is (3sqrt(x)+5x^{3/2})/2
What is the first derivative of xsqrt(x)+x^2sqrt(x) ?
The first derivative of xsqrt(x)+x^2sqrt(x) is (3sqrt(x)+5x^{3/2})/2