What is the derivative of y=ln(7x^2+3y^2) ?

The derivative of y=ln(7x^2+3y^2) is (14x)/(7x^2+3y^2)

What is the first derivative of y=ln(7x^2+3y^2) ?

The first derivative of y=ln(7x^2+3y^2) is (14x)/(7x^2+3y^2)

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

derivative of

y = ln (7 x^{2} + 3 y^{2})

\frac{14 x}{7 x ^{2} + 3 y ^{2}}

Solution steps

\frac{d}{d x} (ln (7 x^{2} + 3 y^{2}))

Treat

y

as a constant

Apply the chain rule:

\frac{1}{7 x ^{2} + 3 y ^{2}} \frac{d}{d x} (7 x^{2} + 3 y^{2})

= \frac{1}{7 x ^{2} + 3 y ^{2}} \frac{d}{d x} (7 x^{2} + 3 y^{2})

\frac{d}{d x} (7 x^{2} + 3 y^{2}) = 14 x

= \frac{1}{7 x ^{2} + 3 y ^{2}} \cdot 14 x

Simplify

\frac{1}{7 x ^{2} + 3 y ^{2}} \cdot 14 x : \frac{14 x}{7 x ^{2} + 3 y ^{2}}

= \frac{14 x}{7 x ^{2} + 3 y ^{2}}

What is the derivative of y=ln(7x^2+3y^2) ?
The derivative of y=ln(7x^2+3y^2) is (14x)/(7x^2+3y^2)
What is the first derivative of y=ln(7x^2+3y^2) ?
The first derivative of y=ln(7x^2+3y^2) is (14x)/(7x^2+3y^2)