What is the derivative of x^{1/2}+x^2 ?

The derivative of x^{1/2}+x^2 is (1+4x^{3/2})/(2x^{1/2)}

What is the first derivative of x^{1/2}+x^2 ?

The first derivative of x^{1/2}+x^2 is (1+4x^{3/2})/(2x^{1/2)}

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derivative of

x^{\frac{1}{2}} + x^{2}

\frac{1 + 4 x ^{\frac{3}{2}}}{2 x ^{\frac{1}{2}}}

Solution steps

\frac{d}{d x} (x^{\frac{1}{2}} + x^{2})

Apply the Sum/Difference Rule:

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

= \frac{d}{d x} (x^{\frac{1}{2}}) + \frac{d}{d x} (x^{2})

\frac{d}{d x} (x^{\frac{1}{2}}) = \frac{1}{2 x ^{\frac{1}{2}}}

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

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

Simplify

\frac{1}{2 x ^{\frac{1}{2}}} + 2 x : \frac{1 + 4 x ^{\frac{3}{2}}}{2 x ^{\frac{1}{2}}}

= \frac{1 + 4 x ^{\frac{3}{2}}}{2 x ^{\frac{1}{2}}}

sin^{2} (3 x - 2)

3^{3 - x}

x^{2} + 5 x - 3

(2 x^{2} - 7) 16 w

\frac{d}{d x} (i \cdot x \cdot 1 - 2 x)

What is the derivative of x^{1/2}+x^2 ?
The derivative of x^{1/2}+x^2 is (1+4x^{3/2})/(2x^{1/2)}
What is the first derivative of x^{1/2}+x^2 ?
The first derivative of x^{1/2}+x^2 is (1+4x^{3/2})/(2x^{1/2)}