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Popular Calculus >

derivative of f(y)=ln(5x^2-x+1)

Solution

derivative of

f (y) = ln (5 x^{2} - x + 1)

Solution

\frac{10 x - 1}{5 x ^{2} - x + 1}

Solution steps

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

Apply the chain rule:

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

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

\frac{d}{d x} (5 x^{2} - x + 1) = 10 x - 1

= \frac{1}{5 x ^{2} - x + 1} (10 x - 1)

Simplify

\frac{1}{5 x ^{2} - x + 1} (10 x - 1) : \frac{10 x - 1}{5 x ^{2} - x + 1}

= \frac{10 x - 1}{5 x ^{2} - x + 1}

Graph

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Frequently Asked Questions (FAQ)

What is the derivative of f(y)=ln(5x^2-x+1) ?
The derivative of f(y)=ln(5x^2-x+1) is (10x-1)/(5x^2-x+1)
What is the first derivative of f(y)=ln(5x^2-x+1) ?
The first derivative of f(y)=ln(5x^2-x+1) is (10x-1)/(5x^2-x+1)