What is the derivative of (x-100^3+(x-100)^2+500) ?

The derivative of (x-100^3+(x-100)^2+500) is 3x^2-598x+29800

What is the first derivative of (x-100^3+(x-100)^2+500) ?

The first derivative of (x-100^3+(x-100)^2+500) is 3x^2-598x+29800

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\frac{d}{d x} ((x - 100)^{3} + (x - 100)^{2} + 500)

3 x^{2} - 598 x + 29800

Solution steps

\frac{d}{d x} ((x - 100)^{3} + (x - 100)^{2} + 500)

Simplify

(x - 100)^{3} + (x - 100)^{2} + 500 : x^{3} - 299 x^{2} + 29800 x - 989500

= \frac{d}{d x} (x^{3} - 299 x^{2} + 29800 x - 989500)

Apply the Sum/Difference Rule:

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

= \frac{d}{d x} (x^{3}) - \frac{d}{d x} (299 x^{2}) + \frac{d}{d x} (29800 x) - \frac{d}{d x} (989500)

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

\frac{d}{d x} (299 x^{2}) = 598 x

\frac{d}{d x} (29800 x) = 29800

\frac{d}{d x} (989500) = 0

= 3 x^{2} - 598 x + 29800 - 0

Simplify

= 3 x^{2} - 598 x + 29800

\int 1 - y^{2} d y

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

g (x) = 8 - x

f (x) = (5 x - 1)^{- \frac{1}{6}}, at x = 13

x \to 0 + lim ((\frac{1}{x})^{3 x})

What is the derivative of (x-100^3+(x-100)^2+500) ?
The derivative of (x-100^3+(x-100)^2+500) is 3x^2-598x+29800
What is the first derivative of (x-100^3+(x-100)^2+500) ?
The first derivative of (x-100^3+(x-100)^2+500) is 3x^2-598x+29800