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

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

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

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

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derivative of

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

5 x^{\frac{1}{4}} + 15 x^{\frac{1}{2}} + 3

Solution steps

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

= 5 x^{\frac{1}{4}} + 15 x^{\frac{1}{2}} + 3

\int 1 + (\frac{x}{2} - \frac{1}{2 x})^{2} d x

(1 + \frac{1}{x})^{3}

7 t y^{^{'}} + y = t^{2}

2 t^{2} - 3 t - 1

\int \frac{1}{x ^{2} + 2 ^{2}} d x

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