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Popular >

derivative of f(x)=sqrt(3x^2-5x+6)

Solution

derivative of

f (x) = 3 x^{2} - 5 x + 6

Solution

\frac{6 x - 5}{2 3 x ^{2} - 5 x + 6}

Solution steps

\frac{d}{d x} (3 x^{2} - 5 x + 6)

Apply the chain rule:

\frac{1}{2 3 x ^{2} - 5 x + 6} \frac{d}{d x} (3 x^{2} - 5 x + 6)

= \frac{1}{2 3 x ^{2} - 5 x + 6} \frac{d}{d x} (3 x^{2} - 5 x + 6)

\frac{d}{d x} (3 x^{2} - 5 x + 6) = 6 x - 5

= \frac{1}{2 3 x ^{2} - 5 x + 6} (6 x - 5)

Simplify

\frac{1}{2 3 x ^{2} - 5 x + 6} (6 x - 5) : \frac{6 x - 5}{2 3 x ^{2} - 5 x + 6}

= \frac{6 x - 5}{2 3 x ^{2} - 5 x + 6}

Popular Examples

derivative of (e^x^{cos(x)})

\frac{d}{d x} ((e^{x})^{c o s (x)})

d/(dz)(z^5-e^zln(z))

\frac{d}{d z} (z^{5} - e^{z} ln (z))

integral of 2+6x-3x^2

\int 2 + 6 x - 3 x^{2} d x

integral of (3x^2)/(x^2+2x+1)

\int \frac{3 x ^{2}}{x ^{2} + 2 x + 1} d x

limit as x approaches 0 of (sqrt(x^2))/x

x \to 0 lim (\frac{x ^{2}}{x})

Frequently Asked Questions (FAQ)

What is the derivative of f(x)=sqrt(3x^2-5x+6) ?
The derivative of f(x)=sqrt(3x^2-5x+6) is (6x-5)/(2sqrt(3x^2-5x+6))
What is the first derivative of f(x)=sqrt(3x^2-5x+6) ?
The first derivative of f(x)=sqrt(3x^2-5x+6) is (6x-5)/(2sqrt(3x^2-5x+6))