What is the derivative of f(x)=(3x^2-2x-1)^{3/2} ?

The derivative of f(x)=(3x^2-2x-1)^{3/2} is 3(3x-1)(3x^2-2x-1)^{1/2}

What is the first derivative of f(x)=(3x^2-2x-1)^{3/2} ?

The first derivative of f(x)=(3x^2-2x-1)^{3/2} is 3(3x-1)(3x^2-2x-1)^{1/2}

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derivative of

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

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

Solution steps

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

Apply the chain rule:

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

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

\frac{d}{d x} (3 x^{2} - 2 x - 1) = 6 x - 2

= \frac{3 ( 3 x ^{2} - 2 x - 1 ) ^{\frac{1}{2}}}{2} (6 x - 2)

Simplify

\frac{3 ( 3 x ^{2} - 2 x - 1 ) ^{\frac{1}{2}}}{2} (6 x - 2) : 3 (3 x - 1) (3 x^{2} - 2 x - 1)^{\frac{1}{2}}

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

\int \frac{38}{38 + e ^{x}} d x

\int \frac{3 + u}{1 - u ^{2}} d u

x \to - 5 lim (x^{2} + 5)

What is the derivative of f(x)=(3x^2-2x-1)^{3/2} ?
The derivative of f(x)=(3x^2-2x-1)^{3/2} is 3(3x-1)(3x^2-2x-1)^{1/2}
What is the first derivative of f(x)=(3x^2-2x-1)^{3/2} ?
The first derivative of f(x)=(3x^2-2x-1)^{3/2} is 3(3x-1)(3x^2-2x-1)^{1/2}