Questions: Part 1 - Differentiation Differentiate the following function: f(x)=8 e^x-5 ln (x) f'(x)=

Solution Steps

The function given is \( f(x) = 8e^x - 5\ln(x) \). To differentiate this function, we start by differentiating the exponential term \( 8e^x \). The derivative of \( e^x \) is \( e^x \), so:

\[ \frac{d}{dx}[8e^x] = 8e^x \]

Next, we differentiate the logarithmic term \(-5\ln(x)\). The derivative of \(\ln(x)\) is \(\frac{1}{x}\), so:

\[ \frac{d}{dx}[-5\ln(x)] = -5 \cdot \frac{1}{x} = -\frac{5}{x} \]

Now, we combine the derivatives of the two terms to find the derivative of the entire function:

\[ f'(x) = 8e^x - \frac{5}{x} \]

Final Answer