What is the derivative of 4x^{5/4}+10x^{3/2}+5x ?

The derivative of 4x^{5/4}+10x^{3/2}+5x is 5x^{1/4}+15x^{1/2}+5

What is the first derivative of 4x^{5/4}+10x^{3/2}+5x ?

The first derivative of 4x^{5/4}+10x^{3/2}+5x is 5x^{1/4}+15x^{1/2}+5

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derivative of

4 x^{\frac{5}{4}} + 10 x^{\frac{3}{2}} + 5 x

5 x^{\frac{1}{4}} + 15 x^{\frac{1}{2}} + 5

Solution steps

\frac{d}{d x} (4 x^{\frac{5}{4}} + 10 x^{\frac{3}{2}} + 5 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} (10 x^{\frac{3}{2}}) + \frac{d}{d x} (5 x)

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

\frac{d}{d x} (10 x^{\frac{3}{2}}) = 15 x^{\frac{1}{2}}

\frac{d}{d x} (5 x) = 5

= 5 x^{\frac{1}{4}} + 15 x^{\frac{1}{2}} + 5

What is the derivative of 4x^{5/4}+10x^{3/2}+5x ?
The derivative of 4x^{5/4}+10x^{3/2}+5x is 5x^{1/4}+15x^{1/2}+5
What is the first derivative of 4x^{5/4}+10x^{3/2}+5x ?
The first derivative of 4x^{5/4}+10x^{3/2}+5x is 5x^{1/4}+15x^{1/2}+5