What is (\partial)/(\partial x)(ln(4+e^{3x})) ?

The answer to (\partial)/(\partial x)(ln(4+e^{3x})) is (3e^{3x})/(4+e^{3x)}

Popular >

(\partial)/(\partial x)(ln(4+e^{3x}))

\frac{\partial}{\partial x} (ln (4 + e^{3 x}))

\frac{3 e ^{3 x}}{4 + e ^{3 x}}

Solution steps

\frac{\partial}{\partial x} (ln (4 + e^{3 x}))

Apply the chain rule:

\frac{1}{4 + e ^{3 x}} \frac{\partial}{\partial x} (4 + e^{3 x})

= \frac{1}{4 + e ^{3 x}} \frac{\partial}{\partial x} (4 + e^{3 x})

\frac{\partial}{\partial x} (4 + e^{3 x}) = 3 e^{3 x}

= \frac{1}{4 + e ^{3 x}} \cdot 3 e^{3 x}

Simplify

\frac{1}{4 + e ^{3 x}} \cdot 3 e^{3 x} : \frac{3 e ^{3 x}}{4 + e ^{3 x}}

= \frac{3 e ^{3 x}}{4 + e ^{3 x}}

\frac{\partial}{\partial y} (e^{x} cos (π y))

\frac{\partial}{\partial y} (x^{2} + y^{2} + 2 x y)

\frac{( 6 s + 3 )}{s ^{4} + 5 s ^{2} + 4}

- sin (x) - \frac{1}{2}

4 x + 1

What is (\partial)/(\partial x)(ln(4+e^{3x})) ?
The answer to (\partial)/(\partial x)(ln(4+e^{3x})) is (3e^{3x})/(4+e^{3x)}