What is the derivative of 5x^3+7x^{2.5}-3x+1 ?

The derivative of 5x^3+7x^{2.5}-3x+1 is 15x^2+17.5x^{1.5}-3

What is the first derivative of 5x^3+7x^{2.5}-3x+1 ?

The first derivative of 5x^3+7x^{2.5}-3x+1 is 15x^2+17.5x^{1.5}-3

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\frac{d}{d x} (5 x^{3} + 7 x^{2.5} - 3 x + 1)

15 x^{2} + 17.5 x^{1.5} - 3

Solution steps

\frac{d}{d x} (5 x^{3} + 7 x^{2.5} - 3 x + 1)

Apply the Sum/Difference Rule:

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

= \frac{d}{d x} (5 x^{3}) + \frac{d}{d x} (7 x^{2.5}) - \frac{d}{d x} (3 x) + \frac{d}{d x} (1)

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

\frac{d}{d x} (7 x^{2.5}) = 17.5 x^{1.5}

\frac{d}{d x} (3 x) = 3

\frac{d}{d x} (1) = 0

= 15 x^{2} + 17.5 x^{1.5} - 3 + 0

Simplify

= 15 x^{2} + 17.5 x^{1.5} - 3

What is the derivative of 5x^3+7x^{2.5}-3x+1 ?
The derivative of 5x^3+7x^{2.5}-3x+1 is 15x^2+17.5x^{1.5}-3
What is the first derivative of 5x^3+7x^{2.5}-3x+1 ?
The first derivative of 5x^3+7x^{2.5}-3x+1 is 15x^2+17.5x^{1.5}-3