What is the derivative of-0.0006x(x-15^2(x-40)) ?

The derivative of-0.0006x(x-15^2(x-40)) is -0.0006(4x^3-210x^2+2850x-9000)

What is the first derivative of-0.0006x(x-15^2(x-40)) ?

The first derivative of-0.0006x(x-15^2(x-40)) is -0.0006(4x^3-210x^2+2850x-9000)

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\frac{d}{d x} (- 0.0006 x (x - 15)^{2} (x - 40))

- 0.0006 (4 x^{3} - 210 x^{2} + 2850 x - 9000)

Solution steps

\frac{d}{d x} (- 0.0006 x (x - 15)^{2} (x - 40))

Take the constant out:

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

= - 0.0006 \frac{d}{d x} (x (x - 15)^{2} (x - 40))

Apply the Product Rule:

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

f = x, g = (x - 15)^{2} (x - 40)

= - 0.0006 (\frac{d x}{d x} (x - 15)^{2} (x - 40) + \frac{d}{d x} ((x - 15)^{2} (x - 40)) x)

\frac{d x}{d x} = 1

\frac{d}{d x} ((x - 15)^{2} (x - 40)) = 3 x^{2} - 140 x + 1425

= - 0.0006 (1 \cdot (x - 15)^{2} (x - 40) + (3 x^{2} - 140 x + 1425) x)

Simplify

- 0.0006 (1 \cdot (x - 15)^{2} (x - 40) + (3 x^{2} - 140 x + 1425) x) : - 0.0006 (4 x^{3} - 210 x^{2} + 2850 x - 9000)

= - 0.0006 (4 x^{3} - 210 x^{2} + 2850 x - 9000)

What is the derivative of-0.0006x(x-15^2(x-40)) ?
The derivative of-0.0006x(x-15^2(x-40)) is -0.0006(4x^3-210x^2+2850x-9000)
What is the first derivative of-0.0006x(x-15^2(x-40)) ?
The first derivative of-0.0006x(x-15^2(x-40)) is -0.0006(4x^3-210x^2+2850x-9000)