What is the derivative of sqrt(x^3-100x+1) ?

The derivative of sqrt(x^3-100x+1) is (3x^2-100)/(2sqrt(x^3-100x+1))

What is the first derivative of sqrt(x^3-100x+1) ?

The first derivative of sqrt(x^3-100x+1) is (3x^2-100)/(2sqrt(x^3-100x+1))

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\frac{d}{d x} (x^{3} - 100 x + 1)

\frac{3 x ^{2} - 100}{2 x ^{3} - 100 x + 1}

Solution steps

\frac{d}{d x} (x^{3} - 100 x + 1)

Apply the chain rule:

\frac{1}{2 x ^{3} - 100 x + 1} \frac{d}{d x} (x^{3} - 100 x + 1)

= \frac{1}{2 x ^{3} - 100 x + 1} \frac{d}{d x} (x^{3} - 100 x + 1)

\frac{d}{d x} (x^{3} - 100 x + 1) = 3 x^{2} - 100

= \frac{1}{2 x ^{3} - 100 x + 1} (3 x^{2} - 100)

Simplify

\frac{1}{2 x ^{3} - 100 x + 1} (3 x^{2} - 100) : \frac{3 x ^{2} - 100}{2 x ^{3} - 100 x + 1}

= \frac{3 x ^{2} - 100}{2 x ^{3} - 100 x + 1}

\frac{d ^{2}}{d x ^{2}} (e^{7 x - 4})

\int arctan (2 t) d t

f (x) = x^{4} - 8 x^{3}

f (x) = 3 x^{3} - 9 x

x \to 1 lim (\frac{1 - x ^{2}}{x + 1})

What is the derivative of sqrt(x^3-100x+1) ?
The derivative of sqrt(x^3-100x+1) is (3x^2-100)/(2sqrt(x^3-100x+1))
What is the first derivative of sqrt(x^3-100x+1) ?
The first derivative of sqrt(x^3-100x+1) is (3x^2-100)/(2sqrt(x^3-100x+1))