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Popular >

derivative of f(x)=x^3-6x^2+9x+5

Solution

derivative of

f (x) = x^{3} - 6 x^{2} + 9 x + 5

Solution

3 x^{2} - 12 x + 9

Solution steps

\frac{d}{d x} (x^{3} - 6 x^{2} + 9 x + 5)

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} (5)

\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} (5) = 0

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

Simplify

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

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Frequently Asked Questions (FAQ)

What is the derivative of f(x)=x^3-6x^2+9x+5 ?
The derivative of f(x)=x^3-6x^2+9x+5 is 3x^2-12x+9
What is the first derivative of f(x)=x^3-6x^2+9x+5 ?
The first derivative of f(x)=x^3-6x^2+9x+5 is 3x^2-12x+9