$$ 1 \leftarrow \quad \begin{array}{r} ext { Find } f^{\prime}(x) \ f(x)=6 e^{x}+5 x-\ln x \ f^{\prime}(x)=\square\end{array} $$

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$$ 1 \leftarrow \quad \begin{array}{r}	ext { Find } f^{\prime}(x) \ f(x)=6 e^{x}+5 x-\ln x \ f^{\prime}(x)=\square\end{array} $$

UpStudy AI · Accepted Answer

**Step 1: Differentiate $$6e^x$$**  
Since the derivative of $$e^x$$ is $$e^x$$, by the constant multiple rule:  
$$
\frac{d}{dx}(6e^x) = 6e^x
$$

**Step 2: Differentiate $$5x$$**  
The derivative of $$x$$ is 1, hence:  
$$
\frac{d}{dx}(5x) = 5
$$

**Step 3: Differentiate $$-\ln x$$**  
The derivative of $$\ln x$$ is $$\frac{1}{x}$$, so:  
$$
\frac{d}{dx}(-\ln x) = -\frac{1}{x}
$$

**Step 4: Combine the results**  
Adding the derivatives from Steps 1, 2, and 3 gives:  
$$
f'(x) = 6e^x + 5 - \frac{1}{x}
$$
$$ f'(x) = 6e^x + 5 - \frac{1}{x} $$

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