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Popular >

derivative of 5/3 x^3+x^2-1

Solution

\frac{d}{d x} (\frac{5}{3} x^{3} + x^{2} - 1)

Solution

5 x^{2} + 2 x

Solution steps

\frac{d}{d x} (\frac{5}{3} x^{3} + x^{2} - 1)

Simplify

\frac{5}{3} x^{3} + x^{2} - 1 : \frac{5 x ^{3}}{3} + x^{2} - 1

= \frac{d}{d x} (\frac{5 x ^{3}}{3} + x^{2} - 1)

Apply the Sum/Difference Rule:

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

= \frac{d}{d x} (\frac{5 x ^{3}}{3}) + \frac{d}{d x} (x^{2}) - \frac{d}{d x} (1)

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

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

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

= 5 x^{2} + 2 x - 0

Simplify

= 5 x^{2} + 2 x

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Frequently Asked Questions (FAQ)

What is the derivative of 5/3 x^3+x^2-1 ?
The derivative of 5/3 x^3+x^2-1 is 5x^2+2x
What is the first derivative of 5/3 x^3+x^2-1 ?
The first derivative of 5/3 x^3+x^2-1 is 5x^2+2x