Question

hw10 differentiation rules 1 (targets c1, c5; §3.3)
score: 4/9 answered: 4/9
question 5
if ( f(x)=8e^{x}-9x^{2}+19 ), find ( f(x) ).
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Explanation:

Step1: Recall derivative rules

The derivative of $e^x$ is $e^x$, and the derivative of $x^n$ is $nx^{n - 1}$, and the derivative of a constant is 0.

Step2: Differentiate each term

For the first - term $8e^x$, its derivative is $8e^x$ (since the derivative of $e^x$ is $e^x$ and by the constant - multiple rule). For the second - term $-9x^2$, using the power rule, its derivative is $-9\times2x=-18x$. For the third - term 19 (a constant), its derivative is 0.

Step3: Combine the derivatives

$f'(x)$ is the sum of the derivatives of each term, so $f'(x)=8e^x-18x + 0=8e^x-18x$.

Answer:

$8e^x-18x$