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Popular Calculus >

derivative of p(x)=(x-3)^3-(x-2)^2+31

Solution

derivative of

p (x) = (x - 3)^{3} - (x - 2)^{2} + 31

Solution

3 x^{2} - 20 x + 31

Solution steps

\frac{d}{d x} ((x - 3)^{3} - (x - 2)^{2} + 31)

Simplify

(x - 3)^{3} - (x - 2)^{2} + 31 : x^{3} - 10 x^{2} + 31 x

= \frac{d}{d x} (x^{3} - 10 x^{2} + 31 x)

Apply the Sum/Difference Rule:

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

= \frac{d}{d x} (x^{3}) - \frac{d}{d x} (10 x^{2}) + \frac{d}{d x} (31 x)

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

\frac{d}{d x} (10 x^{2}) = 20 x

\frac{d}{d x} (31 x) = 31

= 3 x^{2} - 20 x + 31

Graph

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\int_{1}^{8} π (x - 1) d x

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Frequently Asked Questions (FAQ)

What is the derivative of p(x)=(x-3)^3-(x-2)^2+31 ?
The derivative of p(x)=(x-3)^3-(x-2)^2+31 is 3x^2-20x+31
What is the first derivative of p(x)=(x-3)^3-(x-2)^2+31 ?
The first derivative of p(x)=(x-3)^3-(x-2)^2+31 is 3x^2-20x+31