What is the derivative of 10sqrt(x)+4x^{3/4} ?

The derivative of 10sqrt(x)+4x^{3/4} is 5/(x^{1/2)}+3/(x^{1/4)}

What is the first derivative of 10sqrt(x)+4x^{3/4} ?

The first derivative of 10sqrt(x)+4x^{3/4} is 5/(x^{1/2)}+3/(x^{1/4)}

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derivative

\frac{5}{x ^{\frac{1}{2}}} + \frac{3}{x ^{\frac{1}{4}}}

Solution steps

\frac{d}{d x} (10 x + 4 x^{\frac{3}{4}})

Apply the Sum/Difference Rule:

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

= \frac{d}{d x} (10 x) + \frac{d}{d x} (4 x^{\frac{3}{4}})

\frac{d}{d x} (10 x) = \frac{5}{x ^{\frac{1}{2}}}

\frac{d}{d x} (4 x^{\frac{3}{4}}) = \frac{3}{x ^{\frac{1}{4}}}

= \frac{5}{x ^{\frac{1}{2}}} + \frac{3}{x ^{\frac{1}{4}}}

What is the derivative of 10sqrt(x)+4x^{3/4} ?
The derivative of 10sqrt(x)+4x^{3/4} is 5/(x^{1/2)}+3/(x^{1/4)}
What is the first derivative of 10sqrt(x)+4x^{3/4} ?
The first derivative of 10sqrt(x)+4x^{3/4} is 5/(x^{1/2)}+3/(x^{1/4)}