What is the derivative of |x^3+8x^2+5x-50| ?

The derivative of |x^3+8x^2+5x-50| is ((x^3+8x^2+5x-50)(3x^2+16x+5))/(|x^3+8x^2+5x-50|)

What is the first derivative of |x^3+8x^2+5x-50| ?

The first derivative of |x^3+8x^2+5x-50| is ((x^3+8x^2+5x-50)(3x^2+16x+5))/(|x^3+8x^2+5x-50|)

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\frac{d}{d x} (x^{3} + 8 x^{2} + 5 x - 50)

\frac{( x ^{3} + 8 x ^{2} + 5 x - 50 ) ( 3 x ^{2} + 16 x + 5 )}{∣ x ^{3} + 8 x ^{2} + 5 x - 50 ∣}

Solution steps

\frac{d}{d x} (x^{3} + 8 x^{2} + 5 x - 50)

Apply the chain rule:

\frac{x ^{3} + 8 x ^{2} + 5 x - 50}{∣ ( x ^{3} + 8 x ^{2} + 5 x - 50 ) ∣} \frac{d}{d x} (x^{3} + 8 x^{2} + 5 x - 50)

= \frac{x ^{3} + 8 x ^{2} + 5 x - 50}{∣ ( x ^{3} + 8 x ^{2} + 5 x - 50 ) ∣} \frac{d}{d x} (x^{3} + 8 x^{2} + 5 x - 50)

\frac{d}{d x} (x^{3} + 8 x^{2} + 5 x - 50) = 3 x^{2} + 16 x + 5

= \frac{x ^{3} + 8 x ^{2} + 5 x - 50}{∣ ( x ^{3} + 8 x ^{2} + 5 x - 50 ) ∣} (3 x^{2} + 16 x + 5)

Multiply fractions:

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

= \frac{( x ^{3} + 8 x ^{2} + 5 x - 50 ) ( 3 x ^{2} + 16 x + 5 )}{∣ x ^{3} + 8 x ^{2} + 5 x - 50 ∣}

What is the derivative of |x^3+8x^2+5x-50| ?
The derivative of |x^3+8x^2+5x-50| is ((x^3+8x^2+5x-50)(3x^2+16x+5))/(|x^3+8x^2+5x-50|)
What is the first derivative of |x^3+8x^2+5x-50| ?
The first derivative of |x^3+8x^2+5x-50| is ((x^3+8x^2+5x-50)(3x^2+16x+5))/(|x^3+8x^2+5x-50|)