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

The derivative of x+xsqrt(x) is 1+(3sqrt(x))/2

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

The first derivative of x+xsqrt(x) is 1+(3sqrt(x))/2

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

1 + \frac{3 x}{2}

Solution steps

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

Simplify

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

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

Apply the Sum/Difference Rule:

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

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

\frac{d x}{d x} = 1

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

= 1 + \frac{3 x}{2}

What is the derivative of x+xsqrt(x) ?
The derivative of x+xsqrt(x) is 1+(3sqrt(x))/2
What is the first derivative of x+xsqrt(x) ?
The first derivative of x+xsqrt(x) is 1+(3sqrt(x))/2