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4. Differentiate the following functions. Show your work. Try to simplify your answers if you can. (Hint: In some cases it might be advantageous to simplify/rewrite first. For part b, 8 is the variable and x is the constant.) a. g(t) = ( ²7 +²³) (²² + 1) r²+hr to b. f(3) = Bx + 6 1-8 C. h(y) = 1 Cos y - sin y

4. Differentiate the following functions. Show your work. Try to simplify your answers if you can. (Hint: In some cases it might be advantageous to simplify/rewrite first. For part b, 8 is the variable and x is the constant.) a. g(t) = ( ²7 +²³) (²² + 1) r²+hr to b. f(3) = Bx + 6 1-8 C. h(y) = 1 Cos y - sin y

Calculus: Early Transcendentals
Calculus: Early Transcendentals
8th Edition
ISBN:9781285741550
Author:James Stewart
Publisher:James Stewart
Chapter1: Functions And Models
Section: Chapter Questions
Problem 1RCC: (a) What is a function? What are its domain and range? (b) What is the graph of a function? (c) How...
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Question 4
**Differentiation Exercise** **4. Differentiate the following functions. Show your work. Try to simplify your answers if you can.** *Hint:* In some cases it might be advantageous to simplify/rewrite first. For part b, \(\beta\) is the variable and \(x\) is the constant. a. \( g(t) = \left(\frac{2}{t} + t^5 \right) (t^3 + 1) \) b. \( f(\beta) = \frac{6x + x^6}{1 - \beta} \) c. \( h(y) = \frac{\cos y}{1 - \sin y} \) d. \( f(x) = \frac{x^2 + bx + c}{a} \) e. \( z(m) = \log_{10} (10^{2m}) \) --- **5. Find the equation of the tangent line to the following function at \(x = \pi/4\).** Write all terms in the tangent-line equation in EXACT FORM, i.e., with square roots and fractions. \( p(x) = \sin x \tan x \)
Transcribed Image Text:**Differentiation Exercise** **4. Differentiate the following functions. Show your work. Try to simplify your answers if you can.** *Hint:* In some cases it might be advantageous to simplify/rewrite first. For part b, \(\beta\) is the variable and \(x\) is the constant. a. \( g(t) = \left(\frac{2}{t} + t^5 \right) (t^3 + 1) \) b. \( f(\beta) = \frac{6x + x^6}{1 - \beta} \) c. \( h(y) = \frac{\cos y}{1 - \sin y} \) d. \( f(x) = \frac{x^2 + bx + c}{a} \) e. \( z(m) = \log_{10} (10^{2m}) \) --- **5. Find the equation of the tangent line to the following function at \(x = \pi/4\).** Write all terms in the tangent-line equation in EXACT FORM, i.e., with square roots and fractions. \( p(x) = \sin x \tan x \)
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As per our company guidelines we are supposed to answer only first three sub-parts. Kindly repost other parts in next question.

Given problems:-

a) gt=2t+t5t3+1

b) fβ=βx+x61-β

c) hy=cosy1-siny

 

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