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Popular >

derivative of f(x)=4x^{5/4}+4x^{3/2}+8x

Solution

derivative of

f (x) = 4 x^{\frac{5}{4}} + 4 x^{\frac{3}{2}} + 8 x

Solution

5 x^{\frac{1}{4}} + 6 x^{\frac{1}{2}} + 8

Solution steps

\frac{d}{d x} (4 x^{\frac{5}{4}} + 4 x^{\frac{3}{2}} + 8 x)

Apply the Sum/Difference Rule:

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

= \frac{d}{d x} (4 x^{\frac{5}{4}}) + \frac{d}{d x} (4 x^{\frac{3}{2}}) + \frac{d}{d x} (8 x)

\frac{d}{d x} (4 x^{\frac{5}{4}}) = 5 x^{\frac{1}{4}}

\frac{d}{d x} (4 x^{\frac{3}{2}}) = 6 x^{\frac{1}{2}}

\frac{d}{d x} (8 x) = 8

= 5 x^{\frac{1}{4}} + 6 x^{\frac{1}{2}} + 8

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Frequently Asked Questions (FAQ)

What is the derivative of f(x)=4x^{5/4}+4x^{3/2}+8x ?
The derivative of f(x)=4x^{5/4}+4x^{3/2}+8x is 5x^{1/4}+6x^{1/2}+8
What is the first derivative of f(x)=4x^{5/4}+4x^{3/2}+8x ?
The first derivative of f(x)=4x^{5/4}+4x^{3/2}+8x is 5x^{1/4}+6x^{1/2}+8