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

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

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

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

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derivative of

y = \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{d}{d t} (40 - 8 t)

x^{2} \cdot 1 + x^{2}

(3 x^{2} + 5)^{9}

\frac{d}{d x} (\frac{( x - y )}{y _{2} ( x )})

2 cos^{2} (\frac{t}{2})

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