What is the derivative of 7x^{1/2}+x^{3/2} ?

The derivative of 7x^{1/2}+x^{3/2} is 7/(2x^{1/2)}+(3x^{1/2})/2

What is the first derivative of 7x^{1/2}+x^{3/2} ?

The first derivative of 7x^{1/2}+x^{3/2} is 7/(2x^{1/2)}+(3x^{1/2})/2

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\frac{d}{d x} (7 x^{\frac{1}{2}} + x^{\frac{3}{2}})

\frac{7}{2 x ^{\frac{1}{2}}} + \frac{3 x ^{\frac{1}{2}}}{2}

Solution steps

\frac{d}{d x} (7 x^{\frac{1}{2}} + x^{\frac{3}{2}})

Apply the Sum/Difference Rule:

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

= \frac{d}{d x} (7 x^{\frac{1}{2}}) + \frac{d}{d x} (x^{\frac{3}{2}})

\frac{d}{d x} (7 x^{\frac{1}{2}}) = \frac{7}{2 x ^{\frac{1}{2}}}

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

= \frac{7}{2 x ^{\frac{1}{2}}} + \frac{3 x ^{\frac{1}{2}}}{2}

What is the derivative of 7x^{1/2}+x^{3/2} ?
The derivative of 7x^{1/2}+x^{3/2} is 7/(2x^{1/2)}+(3x^{1/2})/2
What is the first derivative of 7x^{1/2}+x^{3/2} ?
The first derivative of 7x^{1/2}+x^{3/2} is 7/(2x^{1/2)}+(3x^{1/2})/2