What is the derivative of |x^3+10x^2+25x| ?

The derivative of |x^3+10x^2+25x| is ((x^3+10x^2+25x)(3x^2+20x+25))/(|x^3+10x^2+25x|)

What is the first derivative of |x^3+10x^2+25x| ?

The first derivative of |x^3+10x^2+25x| is ((x^3+10x^2+25x)(3x^2+20x+25))/(|x^3+10x^2+25x|)

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\frac{d}{d x} (x^{3} + 10 x^{2} + 25 x)

\frac{( x ^{3} + 10 x ^{2} + 25 x ) ( 3 x ^{2} + 20 x + 25 )}{∣ x ^{3} + 10 x ^{2} + 25 x ∣}

Solution steps

\frac{d}{d x} (x^{3} + 10 x^{2} + 25 x)

Apply the chain rule:

\frac{x ^{3} + 10 x ^{2} + 25 x}{∣ ( x ^{3} + 10 x ^{2} + 25 x ) ∣} \frac{d}{d x} (x^{3} + 10 x^{2} + 25 x)

= \frac{x ^{3} + 10 x ^{2} + 25 x}{∣ ( x ^{3} + 10 x ^{2} + 25 x ) ∣} \frac{d}{d x} (x^{3} + 10 x^{2} + 25 x)

\frac{d}{d x} (x^{3} + 10 x^{2} + 25 x) = 3 x^{2} + 20 x + 25

= \frac{x ^{3} + 10 x ^{2} + 25 x}{∣ ( x ^{3} + 10 x ^{2} + 25 x ) ∣} (3 x^{2} + 20 x + 25)

Multiply fractions:

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

= \frac{( x ^{3} + 10 x ^{2} + 25 x ) ( 3 x ^{2} + 20 x + 25 )}{∣ x ^{3} + 10 x ^{2} + 25 x ∣}

What is the derivative of |x^3+10x^2+25x| ?
The derivative of |x^3+10x^2+25x| is ((x^3+10x^2+25x)(3x^2+20x+25))/(|x^3+10x^2+25x|)
What is the first derivative of |x^3+10x^2+25x| ?
The first derivative of |x^3+10x^2+25x| is ((x^3+10x^2+25x)(3x^2+20x+25))/(|x^3+10x^2+25x|)