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Popular Calculus >

derivative of y=ln(8x^2-7x+9)

Solution

derivative of

y = ln (8 x^{2} - 7 x + 9)

Solution

\frac{16 x - 7}{8 x ^{2} - 7 x + 9}

Solution steps

\frac{d}{d x} (ln (8 x^{2} - 7 x + 9))

Apply the chain rule:

\frac{1}{8 x ^{2} - 7 x + 9} \frac{d}{d x} (8 x^{2} - 7 x + 9)

= \frac{1}{8 x ^{2} - 7 x + 9} \frac{d}{d x} (8 x^{2} - 7 x + 9)

\frac{d}{d x} (8 x^{2} - 7 x + 9) = 16 x - 7

= \frac{1}{8 x ^{2} - 7 x + 9} (16 x - 7)

Simplify

\frac{1}{8 x ^{2} - 7 x + 9} (16 x - 7) : \frac{16 x - 7}{8 x ^{2} - 7 x + 9}

= \frac{16 x - 7}{8 x ^{2} - 7 x + 9}

Graph

Popular Examples

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d er i v a t i v e f (t) = e^{9 t s i n (2 t)}

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d er i v a t i v e \frac{x ^{2}}{x + 8}

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(\partial)/(\partial x)(sin(x^3)+3xy)

\frac{\partial}{\partial x} (sin (x^{3}) + 3 x y)

Frequently Asked Questions (FAQ)

What is the derivative of y=ln(8x^2-7x+9) ?
The derivative of y=ln(8x^2-7x+9) is (16x-7)/(8x^2-7x+9)
What is the first derivative of y=ln(8x^2-7x+9) ?
The first derivative of y=ln(8x^2-7x+9) is (16x-7)/(8x^2-7x+9)