3
Evaluate the derivative of \(f(x)=\cos(5x+3)\text{.}\)
4
Evaluate the derivative of \(f(x)=\left({x^2+2}\right)^5\text{.}\)
5
Evaluate the derivative of \(T(k)=\left({4k^4+2k^2+1}\right)^{17}\text{.}\)
6
Evaluate the derivative of \(f(x)=\sqrt{\dfrac{x^2+1}{x^2-1}}\text{.}\)
7
Evaluate the derivative of \(f(x)=e^{\cos(x^2)}\text{.}\)
8 (✳)
Evaluate \(f'(2)\) if \(f(x) = g\big(x/h(x)\big)\text{,}\) \(h(2) = 2\text{,}\) \(h'(2) = 3\text{,}\) \(g'(1) = 4\text{.}\)
9 (✳)
Find the derivative of \(e^{x\cos(x)}\text{.}\)
10 (✳)
Evaluate \(f'(x)\) if \(f(x) = e^{x^2+\cos x}\text{.}\)
11 (✳)
Evaluate \(f'(x)\) if \(f(x) = \sqrt{\dfrac{x-1}{x+2}}\text{.}\)
12 (✳)
Differentiate the function
\begin{equation*}
f(x)=\frac{1}{x^2}+\sqrt{x^2-1}
\end{equation*}
and give the domain where the derivative exists.
13 (✳)
Evaluate the derivative of \(f(x)=\dfrac{\sin 5x}{1+x^2}\)
14
Evaluate the derivative of \(f(x)=\sec(e^{2x+7})\text{.}\)
15
Find the tangent line to the curve \(y=\left(\tan^2 x +1\right)\left(\cos^2 x\right)\) at the point \(x=\dfrac{\pi}{4}\text{.}\)
16
The position of a particle at time \(t\) is given by \(s(t)=e^{t^3-7t^2+8t}\text{.}\) For which values of \(t\) is the velocity of the particle zero?
17
What is the slope of the tangent line to the curve \(y=\tan\left(e^{x^2}\right)\) at the point \(x=1\text{?}\)
18 (✳)
Differentiate \(y=e^{4x}\tan x\text{.}\) You do not need to simplify your answer.
19 (✳)
Evaluate the derivative of the following function at \(x=1\text{:}\) \(f(x)=\dfrac{x^3}{1+e^{3x}}\text{.}\)
20 (✳)
Differentiate \(e^{\sin^2(x)}\text{.}\)
21 (✳)
Compute the derivative of \(y=\sin\left(e^{5x}\right)\)
22 (✳)
Find the derivative of \(e^{\cos(x^2)}\text{.}\)
23 (✳)
Compute the derivative of \(y=\cos\big(x^2+\sqrt{x^2+1}\big)\)
24 (✳)
Evaluate the derivative.
\begin{equation*}
y=(1+x^2)\cos^2 x
\end{equation*}
25 (✳)
Evaluate the derivative.
\begin{equation*}
y=\frac{e^{3x}}{1+x^2}
\end{equation*}
26 (✳)
Find \(g'(2)\) if \(g(x)=x^3h(x^2)\text{,}\) where \(h(4)=2\) and \(h'(4)=-2\text{.}\)
27 (✳)
At what points \((x,y)\) does the curve \(y=xe^{-(x^2-1)/2}\) have a horizontal tangent?
28
A particle starts moving at time \(t=1\text{,}\) and its position thereafter is given by
\begin{equation*}
s(t)=\sin\left(\frac{1}{t}\right).
\end{equation*}
When is the particle moving in the negative direction?
29
Compute the derivative of \(f(x)=\dfrac{e^{x}}{\cos^3 (5x-7)}\text{.}\)
30 (✳)
Evaluate \(\ds\diff{}{x}\left\{x e^{2x} \cos 4x\right\}\text{.}\)