Question

quiz 7 - requires respondus lockdown browser + we
started: oct 6 at 6:58pm
quiz instructions
access code: start
timed: 25 minutes
number of attempts: 2
content: review of power rule, quotient rule, derivative of trig functions, and related rates
question 3
find the derivative of the function.
f(x) = 7cosx - 4x - 1

• 7 sin x - 4

no correct answer choice is given.

• 7 cos x - 4

7 cos x - 4
7 sin x - 4

Explanation:

Step1: Apply sum - difference rule

The derivative of a sum/difference of functions is the sum/difference of their derivatives. So, $f^\prime(x)=(7\cos x)^\prime-(4x)^\prime-(1)^\prime$.

Step2: Differentiate $7\cos x$

Using the constant - multiple rule $(cf(x))^\prime = cf^\prime(x)$ and the derivative of $\cos x$ which is $-\sin x$, we have $(7\cos x)^\prime = 7(\cos x)^\prime=-7\sin x$.

Step3: Differentiate $4x$

Using the power rule $(x^n)^\prime=nx^{n - 1}$, for $y = 4x=4x^1$, we get $(4x)^\prime=4\times1\times x^{1 - 1}=4$.

Step4: Differentiate the constant 1

The derivative of a constant $c$ is 0, so $(1)^\prime = 0$.

Step5: Combine the results

$f^\prime(x)=-7\sin x-4 - 0=-7\sin x-4$.

Answer:

• 7 sin x - 4