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Popular >

derivative of 1/3 x^3+7x^2+50x

Solution

\frac{d}{d x} (\frac{1}{3} x^{3} + 7 x^{2} + 50 x)

Solution

x^{2} + 14 x + 50

Solution steps

\frac{d}{d x} (\frac{1}{3} x^{3} + 7 x^{2} + 50 x)

Simplify

\frac{1}{3} x^{3} + 7 x^{2} + 50 x : \frac{x ^{3}}{3} + 7 x^{2} + 50 x

= \frac{d}{d x} (\frac{x ^{3}}{3} + 7 x^{2} + 50 x)

Apply the Sum/Difference Rule:

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

= \frac{d}{d x} (\frac{x ^{3}}{3}) + \frac{d}{d x} (7 x^{2}) + \frac{d}{d x} (50 x)

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

\frac{d}{d x} (7 x^{2}) = 14 x

\frac{d}{d x} (50 x) = 50

= x^{2} + 14 x + 50

Popular Examples

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\int \frac{y ^{4}}{y ^{2} - 9} d y

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\int (1 + sin (x)) d x

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(\partial)/(\partial x)(y^2+1)

\frac{\partial}{\partial x} (y^{2} + 1)

integral of tan(x/(sqrt(2)))

\int tan (\frac{x}{2}) d x

Frequently Asked Questions (FAQ)

What is the derivative of 1/3 x^3+7x^2+50x ?
The derivative of 1/3 x^3+7x^2+50x is x^2+14x+50
What is the first derivative of 1/3 x^3+7x^2+50x ?
The first derivative of 1/3 x^3+7x^2+50x is x^2+14x+50