What is the derivative of-(x+3(x-9)^2) ?

The derivative of-(x+3(x-9)^2) is -3x^2+30x-27

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

The first derivative of-(x+3(x-9)^2) is -3x^2+30x-27

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

- 3 x^{2} + 30 x - 27

Solution steps

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

Take the constant out:

(a \cdot f)^{'} = a \cdot f^{'}

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

Apply the Product Rule:

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

f = x + 3, g = (x - 9)^{2}

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

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

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

= - (1 \cdot (x - 9)^{2} + 2 (x - 9) (x + 3))

Simplify

- (1 \cdot (x - 9)^{2} + 2 (x - 9) (x + 3)) : - 3 x^{2} + 30 x - 27

= - 3 x^{2} + 30 x - 27

\int x \cdot e^{x y} d y

\int 16 x e^{4 x} d x

x^{2} + 16

3 x^{3} - 12 x^{2} + 15 x

f (t) = t^{2}

What is the derivative of-(x+3(x-9)^2) ?
The derivative of-(x+3(x-9)^2) is -3x^2+30x-27
What is the first derivative of-(x+3(x-9)^2) ?
The first derivative of-(x+3(x-9)^2) is -3x^2+30x-27