What is the derivative of ln(5x^2+7y^2) ?

The derivative of ln(5x^2+7y^2) is (10x)/(5x^2+7y^2)

What is the first derivative of ln(5x^2+7y^2) ?

The first derivative of ln(5x^2+7y^2) is (10x)/(5x^2+7y^2)

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derivative of

ln (5 x^{2} + 7 y^{2})

\frac{10 x}{5 x ^{2} + 7 y ^{2}}

Solution steps

\frac{d}{d x} (ln (5 x^{2} + 7 y^{2}))

Treat

y

as a constant

Apply the chain rule:

\frac{1}{5 x ^{2} + 7 y ^{2}} \frac{d}{d x} (5 x^{2} + 7 y^{2})

= \frac{1}{5 x ^{2} + 7 y ^{2}} \frac{d}{d x} (5 x^{2} + 7 y^{2})

\frac{d}{d x} (5 x^{2} + 7 y^{2}) = 10 x

= \frac{1}{5 x ^{2} + 7 y ^{2}} \cdot 10 x

Simplify

\frac{1}{5 x ^{2} + 7 y ^{2}} \cdot 10 x : \frac{10 x}{5 x ^{2} + 7 y ^{2}}

= \frac{10 x}{5 x ^{2} + 7 y ^{2}}

f (x) = 1 + 5 e^{x}, at x = 1

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

x y + y^{2} + x^{2} - x^{2} y^{^{'}} = 0

\int sin (105 x) sin (45 x) d x

y = 2 x^{3} + 3 x^{2} - 12 x + 8

What is the derivative of ln(5x^2+7y^2) ?
The derivative of ln(5x^2+7y^2) is (10x)/(5x^2+7y^2)
What is the first derivative of ln(5x^2+7y^2) ?
The first derivative of ln(5x^2+7y^2) is (10x)/(5x^2+7y^2)