What is the derivative of f(x)=|x^2-25| ?

The derivative of f(x)=|x^2-25| is (2x(x^2-25))/(|x^2-25|)

What is the first derivative of f(x)=|x^2-25| ?

The first derivative of f(x)=|x^2-25| is (2x(x^2-25))/(|x^2-25|)

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derivative of

f (x) = x^{2} - 25

\frac{2 x ( x ^{2} - 25 )}{∣ x ^{2} - 25 ∣}

Solution steps

\frac{d}{d x} (x^{2} - 25)

Apply the chain rule:

\frac{x ^{2} - 25}{∣ ( x ^{2} - 25 ) ∣} \frac{d}{d x} (x^{2} - 25)

= \frac{x ^{2} - 25}{∣ ( x ^{2} - 25 ) ∣} \frac{d}{d x} (x^{2} - 25)

\frac{d}{d x} (x^{2} - 25) = 2 x

= \frac{x ^{2} - 25}{∣ ( x ^{2} - 25 ) ∣} \cdot 2 x

Multiply fractions:

a \cdot \frac{b}{c} = \frac{a \cdot b}{c}

= \frac{2 x ( x ^{2} - 25 )}{∣ x ^{2} - 25 ∣}

x \to 0 lim (\frac{sin ( 6 x )}{sin ( 9 x )})

t y^{^{'}} + (t + 1) y = t, y (ln (7)) = 1

\frac{d}{d x} (5 x^{3} + 2 ln (x))

x \to 1 lim (\frac{x - 5}{x - 1})

\frac{d}{d x} (e^{(x^{2} + x)})

What is the derivative of f(x)=|x^2-25| ?
The derivative of f(x)=|x^2-25| is (2x(x^2-25))/(|x^2-25|)
What is the first derivative of f(x)=|x^2-25| ?
The first derivative of f(x)=|x^2-25| is (2x(x^2-25))/(|x^2-25|)