What is the derivative of y=ln(5x^2+3y^2) ?

The derivative of y=ln(5x^2+3y^2) is (10x)/(5x^2+3y^2)

What is the first derivative of y=ln(5x^2+3y^2) ?

The first derivative of y=ln(5x^2+3y^2) is (10x)/(5x^2+3y^2)

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derivative of

y = ln (5 x^{2} + 3 y^{2})

\frac{10 x}{5 x ^{2} + 3 y ^{2}}

Solution steps

\frac{d}{d x} (ln (5 x^{2} + 3 y^{2}))

Treat

y

as a constant

Apply the chain rule:

\frac{1}{5 x ^{2} + 3 y ^{2}} \frac{d}{d x} (5 x^{2} + 3 y^{2})

= \frac{1}{5 x ^{2} + 3 y ^{2}} \frac{d}{d x} (5 x^{2} + 3 y^{2})

\frac{d}{d x} (5 x^{2} + 3 y^{2}) = 10 x

= \frac{1}{5 x ^{2} + 3 y ^{2}} \cdot 10 x

Simplify

\frac{1}{5 x ^{2} + 3 y ^{2}} \cdot 10 x : \frac{10 x}{5 x ^{2} + 3 y ^{2}}

= \frac{10 x}{5 x ^{2} + 3 y ^{2}}

x \to 4 + lim (\frac{2 x}{x - 4})

\int \frac{tan ^{3} ( \frac{7}{z} )}{z ^{2}} d z

\frac{\partial}{\partial z} (x e^{2 yz})

\frac{\partial}{\partial x} (\frac{2}{( x - 3 t ) ^{2} + 1})

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

What is the derivative of y=ln(5x^2+3y^2) ?
The derivative of y=ln(5x^2+3y^2) is (10x)/(5x^2+3y^2)
What is the first derivative of y=ln(5x^2+3y^2) ?
The first derivative of y=ln(5x^2+3y^2) is (10x)/(5x^2+3y^2)