What is (\partial)/(\partial x)(ln(5x^2+4y^2+9)) ?

The answer to (\partial)/(\partial x)(ln(5x^2+4y^2+9)) is (10x)/(5x^2+4y^2+9)

Popular >

(\partial)/(\partial x)(ln(5x^2+4y^2+9))

\frac{\partial}{\partial x} (ln (5 x^{2} + 4 y^{2} + 9))

\frac{10 x}{5 x ^{2} + 4 y ^{2} + 9}

Solution steps

\frac{\partial}{\partial x} (ln (5 x^{2} + 4 y^{2} + 9))

Treat

y

as a constant

Apply the chain rule:

\frac{1}{5 x ^{2} + 4 y ^{2} + 9} \frac{\partial}{\partial x} (5 x^{2} + 4 y^{2} + 9)

= \frac{1}{5 x ^{2} + 4 y ^{2} + 9} \frac{\partial}{\partial x} (5 x^{2} + 4 y^{2} + 9)

\frac{\partial}{\partial x} (5 x^{2} + 4 y^{2} + 9) = 10 x

= \frac{1}{5 x ^{2} + 4 y ^{2} + 9} \cdot 10 x

Simplify

\frac{1}{5 x ^{2} + 4 y ^{2} + 9} \cdot 10 x : \frac{10 x}{5 x ^{2} + 4 y ^{2} + 9}

= \frac{10 x}{5 x ^{2} + 4 y ^{2} + 9}

\int \frac{12 x ^{3}}{2 - x ^{4}} d x

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

\int_{- 3}^{3} x^{2} + y^{2} d y

x \to 4 lim (3 x - 7)

sin (x) + csc (x)

What is (\partial)/(\partial x)(ln(5x^2+4y^2+9)) ?
The answer to (\partial)/(\partial x)(ln(5x^2+4y^2+9)) is (10x)/(5x^2+4y^2+9)