Derivatives – tan, cot, csc, sec

Trig derivatives are used to find rates of change for sine, cosine, tangent, cotangent, secant, and cosecant functions. The six basic trig derivative rules are important to memorize because they show up often in Calculus 1. These practice problems include constant multiples, basic trig derivatives, chain rule variations, and products involving trig functions.

Notes

Derivatives of Trigonometric Functions

 

Practice Problems

\(\textbf{1)}\) \(f(x)=5\sec x\)

 

\(\textbf{2)}\) \(f(x)=5\cot x\)

 

\(\textbf{3)}\) \(f(x)=5 \csc x\)

 

\(\textbf{4)}\) \(f(x)=5 \tan x\)

 

\(\textbf{5)}\) \(f(x)=5 \sin x\)

 

\(\textbf{6)}\) \(f(x)=5 \cos x\)

 

\(\textbf{7)}\) \(f(x)=7\sec x\)

 

\(\textbf{8)}\) \(f(x)=3 \cot x\)

 

\(\textbf{9)}\) \(f(x)=7 \csc x\)

 

\(\textbf{10)}\) \(f(x)=4\sin x-2\cos x\)

 

\(\textbf{11)}\) \(f(x)=6\tan x+5\sec x\)

 

\(\textbf{12)}\) \(f(x)=3\csc x-8\cot x\)

 

\(\textbf{13)}\) \(f(x)=\sin(4x)\)

 

\(\textbf{14)}\) \(f(x)=\cos(3x^2)\)

 

\(\textbf{15)}\) \(f(x)=\tan(5x)\)

 

\(\textbf{16)}\) \(f(x)=\sec(x^2+1)\)

 

\(\textbf{17)}\) \(f(x)=x^2\sin x\)

 

\(\textbf{18)}\) \(f(x)=e^x\cos x\)

 

\(\textbf{19)}\) \(f(x)=\ln x \tan x\)

 

\(\textbf{20)}\) \(f(x)=\displaystyle\frac{\sin x}{x}\)

 

 

See Related Pages\(\)

\(\bullet\text{Trig Derivative Calculator }\)
\(\,\,\,\,\,\,\,\,\text{(Symbolab.com)}\)
\(\bullet\text{ Calculus Homepage}\)
\(\,\,\,\,\,\,\,\,\text{All the Best Topics…}\)
\(\bullet\text{ Definition of Derivative}\)
\(\,\,\,\,\,\,\,\, \displaystyle \lim_{\Delta x\to 0} \frac{f(x+ \Delta x)-f(x)}{\Delta x} \)
\(\bullet\text{ Equation of the Tangent Line}\)
\(\,\,\,\,\,\,\,\,f(x)=x^3+3x^2−x \text{ at the point } (2,18)\)
\(\bullet\text{ Derivatives- Constant Rule}\)
\(\,\,\,\,\,\,\,\,\displaystyle\frac{d}{dx}(c)=0\)
\(\bullet\text{ Derivatives- Power Rule}\)
\(\,\,\,\,\,\,\,\,\displaystyle\frac{d}{dx}(x^n)=nx^{n-1}\)
\(\bullet\text{ Derivatives- Constant Multiple Rule}\)
\(\,\,\,\,\,\,\,\,\displaystyle\frac{d}{dx}(cf(x))=cf'(x)\)
\(\bullet\text{ Derivatives- Sum and Difference Rules}\)
\(\,\,\,\,\,\,\,\,\displaystyle\frac{d}{dx}[f(x) \pm g(x)]=f'(x) \pm g'(x)\)
\(\bullet\text{ Derivatives- Sin and Cos}\)
\(\,\,\,\,\,\,\,\,\displaystyle\frac{d}{dx}sin(x)=cos(x)\)
\(\bullet\text{ Derivatives- Product Rule}\)
\(\,\,\,\,\,\,\,\,\displaystyle\frac{d}{dx}[f(x) \cdot g(x)]=f(x) \cdot g'(x)+f'(x) \cdot g(x)\)
\(\bullet\text{ Derivatives- Quotient Rule}\)
\(\,\,\,\,\,\,\,\,\displaystyle\frac{d}{dx}\left[\displaystyle\frac{f(x)}{g(x)}\right]=\displaystyle\frac{g(x) \cdot f'(x)-f(x) \cdot g'(x)}{[g(x)]^2}\)
\(\bullet\text{ Derivatives- Chain Rule}\)
\(\,\,\,\,\,\,\,\,\displaystyle\frac{d}{dx}[f(g(x))]= f'(g(x)) \cdot g'(x)\)
\(\bullet\text{ Derivatives- ln(x)}\)
\(\,\,\,\,\,\,\,\,\displaystyle\frac{d}{dx}[ln(x)]= \displaystyle \frac{1}{x}\)
\(\bullet\text{ Implicit Differentiation}\)
\(\,\,\,\,\,\,\,\,\)
\(\bullet\text{ Horizontal Tangent Line}\)
\(\,\,\,\,\,\,\,\,\)
\(\bullet\text{ Mean Value Theorem}\)
\(\,\,\,\,\,\,\,\,\)
\(\bullet\text{ Related Rates}\)
\(\,\,\,\,\,\,\,\,\)
\(\bullet\text{ Increasing and Decreasing Intervals}\)
\(\,\,\,\,\,\,\,\,\)
\(\bullet\text{ Intervals of concave up and down}\)
\(\,\,\,\,\,\,\,\,\)
\(\bullet\text{ Inflection Points}\)
\(\,\,\,\,\,\,\,\,\)
\(\bullet\text{ Graph of f(x), f'(x) and f”(x)}\)
\(\,\,\,\,\,\,\,\,\)Thumbnail for Graphs of First and Second Derivatives
\(\bullet\text{ Newton’s Method}\)
\(\,\,\,\,\,\,\,\,x_{n+1}=x_n – \displaystyle \frac{f(x_n)}{f'(x_n)}\)

 

Scroll to Top