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

The derivative of f(x)=4x^4-3x^{5/2}+2 is 16x^3-(15x^{3/2})/2

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

The first derivative of f(x)=4x^4-3x^{5/2}+2 is 16x^3-(15x^{3/2})/2

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derivative of

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

16 x^{3} - \frac{15 x ^{\frac{3}{2}}}{2}

Solution steps

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

Apply the Sum/Difference Rule:

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

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

\frac{d}{d x} (4 x^{4}) = 16 x^{3}

\frac{d}{d x} (3 x^{\frac{5}{2}}) = \frac{15 x ^{\frac{3}{2}}}{2}

\frac{d}{d x} (2) = 0

= 16 x^{3} - \frac{15 x ^{\frac{3}{2}}}{2} + 0

Simplify

= 16 x^{3} - \frac{15 x ^{\frac{3}{2}}}{2}

What is the derivative of f(x)=4x^4-3x^{5/2}+2 ?
The derivative of f(x)=4x^4-3x^{5/2}+2 is 16x^3-(15x^{3/2})/2
What is the first derivative of f(x)=4x^4-3x^{5/2}+2 ?
The first derivative of f(x)=4x^4-3x^{5/2}+2 is 16x^3-(15x^{3/2})/2