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

The derivative of (x-3^3+3(x-3)^2+6) is 3x^2-12x+9

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

The first derivative of (x-3^3+3(x-3)^2+6) is 3x^2-12x+9

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

3 x^{2} - 12 x + 9

Solution steps

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

Simplify

(x - 3)^{3} + 3 (x - 3)^{2} + 6 : x^{3} - 6 x^{2} + 9 x + 6

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

Apply the Sum/Difference Rule:

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

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

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

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

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

\frac{d}{d x} (6) = 0

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

Simplify

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

\int \frac{4 x ^{4} + x + 1}{x ^{5} + x ^{4}} d x

d er i v a t i v e ln (225 sin^{2} (x))

t an g e n t y = \frac{1}{x}

\int_{1}^{\infty} x^{- 3} d x

y^{^{'}} - 5 y = 4 e^{7 t}

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