What is the derivative of x^2sqrt(x)-5x ?

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

What is the first derivative of x^2sqrt(x)-5x ?

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

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\frac{d}{d x} (x^{2} x - 5 x)

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

Solution steps

\frac{d}{d x} (x^{2} x - 5 x)

Simplify

x^{2} x - 5 x : x^{\frac{5}{2}} - 5 x

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

Apply the Sum/Difference Rule:

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

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

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

\frac{d}{d x} (5 x) = 5

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

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