Derivative of a sum of exponential, logarithmic, and power terms

Apply the sum/difference rule to differentiate each term separately: $h'(x) = \frac{d}{dx}[4e^x] - \frac{d}{dx}[3\ln x] + \frac{d}{dx}[7x^2]$. Using the constant multiple rule, pull the constants out front of each derivative.

Now use known derivative facts: $\frac{d}{dx}[e^x] = e^x$, $\frac{d}{dx}[\ln x] = \frac{1}{x}$, and the power rule gives $\frac{d}{dx}[x^2] = 2x$. Combining these gives $h'(x) = 4e^x - \frac{3}{x} + 14x$. Substituting $x=1$: $h'(1) = 4e^1 - \frac{3}{1} + 14(1) = 4e - 3 + 14 = 4e + 11$.