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Popular >

derivative of 2x^3-42x^2+78x+k

Solution

\frac{d}{d x} (2 x^{3} - 42 x^{2} + 78 x + k)

Solution

6 x^{2} - 84 x + 78

Solution steps

\frac{d}{d x} (2 x^{3} - 42 x^{2} + 78 x + k)

Apply the Sum/Difference Rule:

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

= \frac{d}{d x} (2 x^{3}) - \frac{d}{d x} (42 x^{2}) + \frac{d}{d x} (78 x) + \frac{d k}{d x}

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

\frac{d}{d x} (42 x^{2}) = 84 x

\frac{d}{d x} (78 x) = 78

\frac{d k}{d x} = 0

= 6 x^{2} - 84 x + 78 + 0

Simplify

= 6 x^{2} - 84 x + 78

Popular Examples

limit as t approaches 1 of sqrt(t+1)

t \to 1 lim (t + 1)

limit as x approaches 7 of (3x+2)^{2/3}

x \to 7 lim ((3 x + 2)^{\frac{2}{3}})

integral from 0 to 1 of (1-x)^2x

\int_{0}^{1} (1 - x)^{2} x d x

integral of (3x-2/x)

\int (3 x - \frac{2}{x}) d x

(dy)/(dx)=sqrt(20x+y)-20

\frac{d y}{d x} = 20 x + y - 20

Frequently Asked Questions (FAQ)

What is the derivative of 2x^3-42x^2+78x+k ?
The derivative of 2x^3-42x^2+78x+k is 6x^2-84x+78
What is the first derivative of 2x^3-42x^2+78x+k ?
The first derivative of 2x^3-42x^2+78x+k is 6x^2-84x+78