﻿ Derivatives of Trigonometric Functions and Parametric Equations Worksheet | Problems & Solutions

Derivatives of Trigonometric Functions and Parametric Equations Worksheet

Derivatives of Trigonometric Functions and Parametric Equations Worksheet
• Page 1
1.
What is the derivative of the function $y$ = cosh- 1 ($\sqrt{\frac{x-9}{b-9}}$)?
 a. b. $\sqrt{\frac{b-9}{x-b}}$ c. d.

2.
Find the derivative of ($x$) = $e$sinh- 1 (tan 8$x$).
 a. 8sec 8$x$ $e$sinh- 1 (tan 8$x$) b. cos 8$x$ $e$sinh- 1 (tan 8$x$) c. tan 8$x$ $e$sinh- 1 (tan 8$x$) d. $e$sinh- 1 (tan 8$x$)

3.
Find $\frac{dy}{dx}$ for the parametric curve $x$ = $\frac{8}{t}$, $y$ = $t$ - 23.
 a. - $\frac{1}{8}$ $t$2 b. - $\frac{1}{{t}^{2}}$ c. $t$2 d. $\frac{1}{{t}^{2}}$

4.
Find $\frac{dy}{dx}$ for the parametric curve $x$ = 9$e$5$t$, $y$ = $t$$e$5$t$.
 a. ${e}^{5t}\left(1+5t\right)$ b. 1 + 5$t$ c. $\frac{1+5t}{45}$ d. $\frac{1}{5{e}^{5t}}$

5.
Find the slope of the parametric curve $x$ = 5cos $t$, $y$ = 5sin $t$.
 a. cot $t$ b. - tan $t$ c. - cot $t$ d. tan $t$

6.
Find $\frac{dy}{dx}$ for the parametric curve $x$ = 2$t$2 - 3, $y$ = $t$ + 5.
 a. 4$t$ b. $\frac{1}{4t}$ c. $\frac{1}{4}$ d. $\frac{1}{t}$

7.
Find $\frac{dy}{dx}$ for the parametric curve $x$ = 6$t$, $y$ = 10$t$2.
 a. $t$ b. $\frac{3}{10}$($\frac{1}{t}$) c. $\frac{10}{3}$$t$ d. 1

8.
What is the derivative of $y$ = ?
 a. b. c. cosh $t$ - d. cosh 8$t$

9.
Which of the following is the derivative of ($x$) = $e$cosh2 2$x$?
 a. 4$e$cosh2 2$x$ (cosh 2$x$) b. - $e$cosh2 2$x$ (sinh 4$x$) c. 2$e$cosh2 2$x$ (sinh 4$x$) d. $e$cosh2 4$x$

Which of the following is the derivative of ($x$) = 6tanh 5$x$ + sech 5$x$?
 a. sech 5$x$ (6tanh 5$x$ + sech 5$x$) b. sech 5$x$ (6tanh 5$x$ - sech 5$x$) c. 5sech $x$ (6sech 5$x$ - tanh 5$x$) d. sech 5$x$ (tanh 5$x$ - 6sech 5$x$)