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Popular >

derivative of f(x)=9-|x-4|\at x

Solution

derivative of

f (x) = 9 - ∣ x - 4 ∣ at x

Solution

- \frac{2 x ^{2} - 12 x + 16}{∣ x - 4 ∣}

Solution steps

\frac{d}{d x} (9 - ∣ x - 4 ∣ x)

Apply the Sum/Difference Rule:

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

= \frac{d}{d x} (9) - \frac{d}{d x} (∣ x - 4 ∣ x)

\frac{d}{d x} (9) = 0

\frac{d}{d x} (∣ x - 4 ∣ x) = \frac{2 x ^{2} - 12 x + 16}{∣ x - 4 ∣}

= 0 - \frac{2 x ^{2} - 12 x + 16}{∣ x - 4 ∣}

Simplify

= - \frac{2 x ^{2} - 12 x + 16}{∣ x - 4 ∣}

Popular Examples

limit as x approaches 5-of 2/(x^2-25)

x \to 5 - lim (\frac{2}{x ^{2} - 25})

integral from-2 to 1 of (12x^5-36)

\int_{- 2}^{1} (12 x^{5} - 36) d x

x^2y^{''}+xy^'-y=0,y(1)=1,y^'(1)=4

x^{2} y^{^{''}} + x y^{^{'}} - y = 0, y (1) = 1, y^{^{'}} (1) = 4

integral of (10)/((x+1)(x^2+9))

\int \frac{10}{( x + 1 ) ( x ^{2} + 9 )} d x

simplify (e^{-x}-e^2)(e^x+e^{-5})simplify

(e^{- x} - e^{2}) (e^{x} + e^{- 5})

Frequently Asked Questions (FAQ)

What is the derivative of f(x)=9-|x-4|\at x ?
The derivative of f(x)=9-|x-4|\at x is -(2x^2-12x+16)/(|x-4|)
What is the first derivative of f(x)=9-|x-4|\at x ?
The first derivative of f(x)=9-|x-4|\at x is -(2x^2-12x+16)/(|x-4|)