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Popular >

derivative of f(x)=|x^2-16|

Solution

derivative of

f (x) = x^{2} - 16

Solution

\frac{2 x ( x ^{2} - 16 )}{∣ x ^{2} - 16 ∣}

Solution steps

\frac{d}{d x} (x^{2} - 16)

Apply the chain rule:

\frac{x ^{2} - 16}{∣ ( x ^{2} - 16 ) ∣} \frac{d}{d x} (x^{2} - 16)

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

\frac{d}{d x} (x^{2} - 16) = 2 x

= \frac{x ^{2} - 16}{∣ ( x ^{2} - 16 ) ∣} \cdot 2 x

Multiply fractions:

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

= \frac{2 x ( x ^{2} - 16 )}{∣ x ^{2} - 16 ∣}

Popular Examples

area y= 3/x+2x^3,2<= x<= 3 area

y = \frac{3}{x} + 2 x^{3}, 2 \leq x \leq 3

tangent of f(x)=-2x^3,(1,-2)tangent of

f (x) = - 2 x^{3}, (1, - 2)

derivative of sqrt(x(x+12))

\frac{d}{d x} (x (x + 12))

(\partial)/(\partial x)(3zcos(4xy)+x-7y)

\frac{\partial}{\partial x} (3 z cos (4 x y) + x - 7 y)

derivative of f(x)= 1/(6sqrt(x^3))derivative of

f (x) = \frac{1}{6 x ^{3}}

Frequently Asked Questions (FAQ)

What is the derivative of f(x)=|x^2-16| ?
The derivative of f(x)=|x^2-16| is (2x(x^2-16))/(|x^2-16|)
What is the first derivative of f(x)=|x^2-16| ?
The first derivative of f(x)=|x^2-16| is (2x(x^2-16))/(|x^2-16|)