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Popular >

derivative of ln(x^2-4x+5)

Solution

\frac{d}{d x} (ln (x^{2} - 4 x + 5))

Solution

\frac{2 x - 4}{x ^{2} - 4 x + 5}

Solution steps

\frac{d}{d x} (ln (x^{2} - 4 x + 5))

Apply the chain rule:

\frac{1}{x ^{2} - 4 x + 5} \frac{d}{d x} (x^{2} - 4 x + 5)

= \frac{1}{x ^{2} - 4 x + 5} \frac{d}{d x} (x^{2} - 4 x + 5)

\frac{d}{d x} (x^{2} - 4 x + 5) = 2 x - 4

= \frac{1}{x ^{2} - 4 x + 5} (2 x - 4)

Simplify

\frac{1}{x ^{2} - 4 x + 5} (2 x - 4) : \frac{2 x - 4}{x ^{2} - 4 x + 5}

= \frac{2 x - 4}{x ^{2} - 4 x + 5}

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\frac{\partial}{\partial x} (12 x^{4} - 6 x^{2} y + 4 y^{3})

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Frequently Asked Questions (FAQ)

What is the derivative of ln(x^2-4x+5) ?
The derivative of ln(x^2-4x+5) is (2x-4)/(x^2-4x+5)
What is the first derivative of ln(x^2-4x+5) ?
The first derivative of ln(x^2-4x+5) is (2x-4)/(x^2-4x+5)