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

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

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

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

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derivative of

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

\frac{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{1}{2}})

Apply the chain rule:

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

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

Simplify

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

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

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