What is the derivative of 3x^{1/2}+x^2 ?

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

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

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

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derivative of

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

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

Solution steps

\frac{d}{d x} (3 x^{\frac{1}{2}} + x^{2})

Apply the Sum/Difference Rule:

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

= \frac{d}{d x} (3 x^{\frac{1}{2}}) + \frac{d}{d x} (x^{2})

\frac{d}{d x} (3 x^{\frac{1}{2}}) = \frac{3}{2 x ^{\frac{1}{2}}}

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

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

Simplify

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

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

y = 2 x + cos (x)

y = x (3 - 4 x)

x^{2} - y^{2}

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

\frac{( x - m ^{2} )}{( x + 1 )}

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