What is the derivative of (2^x)/(3^x) ?

The derivative of (2^x)/(3^x) is (2/3)^xln(2/3)

What is the first derivative of (2^x)/(3^x) ?

The first derivative of (2^x)/(3^x) is (2/3)^xln(2/3)

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derivative of

\frac{2 ^{x}}{3 ^{x}}

(\frac{2}{3})^{x} ln (\frac{2}{3})

Solution steps

\frac{d}{d x} (\frac{2 ^{x}}{3 ^{x}})

Simplify

\frac{2 ^{x}}{3 ^{x}} : (\frac{2}{3})^{x}

= \frac{d}{d x} ((\frac{2}{3})^{x})

Apply the derivative exponent rule:

\frac{d}{d x} (a^{x}) = a^{x} ln (a)

= (\frac{2}{3})^{x} ln (\frac{2}{3})

\frac{( x + 1 )}{( x + 2 ) ^{2}}

y = (x^{2} + 2 x)^{2}

\frac{d}{d x} (\frac{1}{2 \cdot ln ( x ^{2} + y ^{2} )})

\frac{d}{d x} (x + 2 y + 3 z)

y^{3} (x^{2} + 2)

What is the derivative of (2^x)/(3^x) ?
The derivative of (2^x)/(3^x) is (2/3)^xln(2/3)
What is the first derivative of (2^x)/(3^x) ?
The first derivative of (2^x)/(3^x) is (2/3)^xln(2/3)