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Popular Calculus >

derivative of p(x)=2x^4+3x^3-6x^2+9

Solution

derivative of

p (x) = 2 x^{4} + 3 x^{3} - 6 x^{2} + 9

Solution

8 x^{3} + 9 x^{2} - 12 x

Solution steps

\frac{d}{d x} (2 x^{4} + 3 x^{3} - 6 x^{2} + 9)

Apply the Sum/Difference Rule:

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

= \frac{d}{d x} (2 x^{4}) + \frac{d}{d x} (3 x^{3}) - \frac{d}{d x} (6 x^{2}) + \frac{d}{d x} (9)

\frac{d}{d x} (2 x^{4}) = 8 x^{3}

\frac{d}{d x} (3 x^{3}) = 9 x^{2}

\frac{d}{d x} (6 x^{2}) = 12 x

\frac{d}{d x} (9) = 0

= 8 x^{3} + 9 x^{2} - 12 x + 0

Simplify

= 8 x^{3} + 9 x^{2} - 12 x

Graph

Popular Examples

derivative of 4cos(3x-3sin(4x))

\frac{d}{d x} (4 cos (3 x) - 3 sin (4 x))

derivative of sin(x^3+3)

\frac{d}{d x} (sin (x^{3} + 3))

derivative of 9sin(x)

\frac{d}{d x} (9 sin (x))

derivative of 2x^{-1}

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

integral from 4 to 6 of y/(y^2-3)

\int_{4}^{6} \frac{y}{y ^{2} - 3} d y

Frequently Asked Questions (FAQ)

What is the derivative of p(x)=2x^4+3x^3-6x^2+9 ?
The derivative of p(x)=2x^4+3x^3-6x^2+9 is 8x^3+9x^2-12x
What is the first derivative of p(x)=2x^4+3x^3-6x^2+9 ?
The first derivative of p(x)=2x^4+3x^3-6x^2+9 is 8x^3+9x^2-12x