What is the derivative of (x-3(x^2+6)) ?

The derivative of (x-3(x^2+6)) is 3x^2-6x+6

What is the first derivative of (x-3(x^2+6)) ?

The first derivative of (x-3(x^2+6)) is 3x^2-6x+6

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

3 x^{2} - 6 x + 6

Solution steps

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

Apply the Product Rule:

(f \cdot g)^{'} = f^{'} \cdot g + f \cdot g^{'}

f = x - 3, g = x^{2} + 6

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

\frac{d}{d x} (x - 3) = 1

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

= 1 \cdot (x^{2} + 6) + 2 x (x - 3)

Simplify

1 \cdot (x^{2} + 6) + 2 x (x - 3) : 3 x^{2} - 6 x + 6

= 3 x^{2} - 6 x + 6

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

\frac{d}{d x} (\frac{a}{x} + b x)

(17 - 13) (178)

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

y^{^{'}} = x^{2} - 6 x + 14

What is the derivative of (x-3(x^2+6)) ?
The derivative of (x-3(x^2+6)) is 3x^2-6x+6
What is the first derivative of (x-3(x^2+6)) ?
The first derivative of (x-3(x^2+6)) is 3x^2-6x+6