Question

find the derivative of f(x).
f(x) = -2·7^x - e^x
f(x) =

Explanation:

Step1: Differentiate \(-2\cdot7^{x}\)

Use the formula \(\frac{d}{dx}(a^{x}) = a^{x}\ln a\). Here \(a = 7\), so \(\frac{d}{dx}(-2\cdot7^{x})=-2\cdot7^{x}\ln7\)

Step2: Differentiate \(-e^{x}\)

Use the formula \(\frac{d}{dx}(e^{x}) = e^{x}\). So \(\frac{d}{dx}(-e^{x})=-e^{x}\)

Step3: Combine the derivatives

By the sum - rule of differentiation \((u + v)^\prime=u^\prime + v^\prime\), where \(u=-2\cdot7^{x}\) and \(v = -e^{x}\). Then \(f^\prime(x)=\frac{d}{dx}(-2\cdot7^{x})+\frac{d}{dx}(-e^{x})\)

Answer:

\(-2\cdot7^{x}\ln7 - e^{x}\)