What is the derivative of f(x)=(18e^x)/(7^x) ?

The derivative of f(x)=(18e^x)/(7^x) is (18(1-ln(7))e^x)/(7^x)

What is the first derivative of f(x)=(18e^x)/(7^x) ?

The first derivative of f(x)=(18e^x)/(7^x) is (18(1-ln(7))e^x)/(7^x)

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derivative of

f (x) = \frac{18 e ^{x}}{7 ^{x}}

\frac{18 ( 1 - ln ( 7 ) ) e ^{x}}{7 ^{x}}

Solution steps

\frac{d}{d x} (\frac{18 e ^{x}}{7 ^{x}})

Take the constant out:

(a \cdot f)^{'} = a \cdot f^{'}

= 18 \frac{d}{d x} (\frac{e ^{x}}{7 ^{x}})

Apply the Quotient Rule:

(\frac{f}{g})^{'} = \frac{f ^{'} \cdot g - g ^{'} \cdot f}{g ^{2}}

= 18 \cdot \frac{\frac{d}{d x} ( e ^{x} ) 7 ^{x} - \frac{d}{d x} ( 7 ^{x} ) e ^{x}}{( 7 ^{x} ) ^{2}}

\frac{d}{d x} (e^{x}) = e^{x}

\frac{d}{d x} (7^{x}) = 7^{x} ln (7)

= 18 \cdot \frac{e ^{x} \cdot 7 ^{x} - 7 ^{x} ln ( 7 ) e ^{x}}{( 7 ^{x} ) ^{2}}

Simplify

18 \cdot \frac{e ^{x} \cdot 7 ^{x} - 7 ^{x} ln ( 7 ) e ^{x}}{( 7 ^{x} ) ^{2}} : \frac{18 ( 1 - ln ( 7 ) ) e ^{x}}{7 ^{x}}

= \frac{18 ( 1 - ln ( 7 ) ) e ^{x}}{7 ^{x}}

What is the derivative of f(x)=(18e^x)/(7^x) ?
The derivative of f(x)=(18e^x)/(7^x) is (18(1-ln(7))e^x)/(7^x)
What is the first derivative of f(x)=(18e^x)/(7^x) ?
The first derivative of f(x)=(18e^x)/(7^x) is (18(1-ln(7))e^x)/(7^x)