What is the derivative of f(x)=5e^n(6-ln(n)) ?

The derivative of f(x)=5e^n(6-ln(n)) is 5(e^n(6-ln(n))-(e^n)/n)

What is the first derivative of f(x)=5e^n(6-ln(n)) ?

The first derivative of f(x)=5e^n(6-ln(n)) is 5(e^n(6-ln(n))-(e^n)/n)

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derivative of

f (x) = 5 e^{n} (6 - ln (n))

5 (e^{n} (6 - ln (n)) - \frac{e ^{n}}{n})

Solution steps

\frac{d}{d n} (5 e^{n} (6 - ln (n)))

Take the constant out:

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

= 5 \frac{d}{d n} (e^{n} (6 - ln (n)))

Apply the Product Rule:

(f \cdot g)^{'} = f^{'} \cdot g + f \cdot g^{'}

f = e^{n}, g = 6 - ln (n)

= 5 (\frac{d}{d n} (e^{n}) (6 - ln (n)) + \frac{d}{d n} (6 - ln (n)) e^{n})

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

\frac{d}{d n} (6 - ln (n)) = - \frac{1}{n}

= 5 (e^{n} (6 - ln (n)) + (- \frac{1}{n}) e^{n})

Simplify

5 (e^{n} (6 - ln (n)) + (- \frac{1}{n}) e^{n}) : 5 (e^{n} (6 - ln (n)) - \frac{e ^{n}}{n})

= 5 (e^{n} (6 - ln (n)) - \frac{e ^{n}}{n})

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What is the derivative of f(x)=5e^n(6-ln(n)) ?
The derivative of f(x)=5e^n(6-ln(n)) is 5(e^n(6-ln(n))-(e^n)/n)
What is the first derivative of f(x)=5e^n(6-ln(n)) ?
The first derivative of f(x)=5e^n(6-ln(n)) is 5(e^n(6-ln(n))-(e^n)/n)