What is the derivative of 4x^{5/4}+8x^{3/2}+2x ?

The derivative of 4x^{5/4}+8x^{3/2}+2x is 5x^{1/4}+12x^{1/2}+2

What is the first derivative of 4x^{5/4}+8x^{3/2}+2x ?

The first derivative of 4x^{5/4}+8x^{3/2}+2x is 5x^{1/4}+12x^{1/2}+2

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derivative of

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

5 x^{\frac{1}{4}} + 12 x^{\frac{1}{2}} + 2

Solution steps

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

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

\frac{d}{d x} (8 x^{\frac{3}{2}}) = 12 x^{\frac{1}{2}}

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

= 5 x^{\frac{1}{4}} + 12 x^{\frac{1}{2}} + 2

What is the derivative of 4x^{5/4}+8x^{3/2}+2x ?
The derivative of 4x^{5/4}+8x^{3/2}+2x is 5x^{1/4}+12x^{1/2}+2
What is the first derivative of 4x^{5/4}+8x^{3/2}+2x ?
The first derivative of 4x^{5/4}+8x^{3/2}+2x is 5x^{1/4}+12x^{1/2}+2