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Popular >

derivative of y=2x^3+3x^2-12x+7

Solution

derivative of

y = 2 x^{3} + 3 x^{2} - 12 x + 7

Solution

6 x^{2} + 6 x - 12

Solution steps

\frac{d}{d x} (2 x^{3} + 3 x^{2} - 12 x + 7)

Apply the Sum/Difference Rule:

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

= \frac{d}{d x} (2 x^{3}) + \frac{d}{d x} (3 x^{2}) - \frac{d}{d x} (12 x) + \frac{d}{d x} (7)

\frac{d}{d x} (2 x^{3}) = 6 x^{2}

\frac{d}{d x} (3 x^{2}) = 6 x

\frac{d}{d x} (12 x) = 12

\frac{d}{d x} (7) = 0

= 6 x^{2} + 6 x - 12 + 0

Simplify

= 6 x^{2} + 6 x - 12

Popular Examples

integral of (12x)/(sqrt(1+4x))

\int \frac{12 x}{1 + 4 x} d x

derivative of (x^3/3+x^2+4x-10)

\frac{d}{d x} (\frac{x ^{3}}{3} + x^{2} + 4 x - 10)

integral of sin(2pi)

\int sin (2 π)

limit as x approaches 1-of (x+1)/(1-x)

x \to 1 - lim (\frac{x + 1}{1 - x})

(\partial)/(\partial x)(sqrt(x)y)

\frac{\partial}{\partial x} (x y)

Frequently Asked Questions (FAQ)

What is the derivative of y=2x^3+3x^2-12x+7 ?
The derivative of y=2x^3+3x^2-12x+7 is 6x^2+6x-12
What is the first derivative of y=2x^3+3x^2-12x+7 ?
The first derivative of y=2x^3+3x^2-12x+7 is 6x^2+6x-12