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Differentiate the following: a) y=-x²+x-5 (b) y = 10 + 2 3 (c) y = 2√x - X

Differentiate the following: a) y=-x²+x-5 (b) y = 10 + 2 3 (c) y = 2√x - X

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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**Differentiate the following:** (a) \( y = -x^2 + x - 5 \) (b) \( y = \frac{x^5}{10} - \frac{x^2}{2} + \frac{x}{3} \) (c) \( y = 2 \sqrt{x} - \frac{4}{x^2} \) (d) \( y = (x^2 + 3x) \sin x \) (e) \( y = \frac{4 \cos x}{e^x} \) (f) \( y = \frac{1 + x - 4 \sqrt{x}}{x} \) (g) \( y = x^2 \cot x - \frac{1}{x^2} \) (h) \( y = (\sec x + \tan x)(\sec x - \tan x) \) (i) \( y = (\sin x + \cos x) \sec x \) (j) \( y = \tan x - e^{-x} \) (k) \( y = \frac{\sin x}{\cos x - \sin x} \) (l) \( y = \cos^3 \theta \) (m) \( y = \sin \left( \tan e^{5 \sin x} \right) \) (n) \( y = x^{x^2 \cos^{-2} x} \) (o) \( y = \left( \frac{\sin \theta}{1 + \cos \theta} \right)^2 \) (p) \( y = \sec \sqrt{x} \tan \left( \frac{1}{x} \right) \) (q) \( y = \frac{\cos x - \sin x}{\sin x} \) (r) \( y = \frac{2}{\csc x} + \frac{3}{\cos x} \) These equations represent functions that need to be differentiated with respect to their variables. Differentiation is a fundamental concept in calculus used to determine the rate at which a function is changing at any given point.
Transcribed Image Text:**Differentiate the following:** (a) \( y = -x^2 + x - 5 \) (b) \( y = \frac{x^5}{10} - \frac{x^2}{2} + \frac{x}{3} \) (c) \( y = 2 \sqrt{x} - \frac{4}{x^2} \) (d) \( y = (x^2 + 3x) \sin x \) (e) \( y = \frac{4 \cos x}{e^x} \) (f) \( y = \frac{1 + x - 4 \sqrt{x}}{x} \) (g) \( y = x^2 \cot x - \frac{1}{x^2} \) (h) \( y = (\sec x + \tan x)(\sec x - \tan x) \) (i) \( y = (\sin x + \cos x) \sec x \) (j) \( y = \tan x - e^{-x} \) (k) \( y = \frac{\sin x}{\cos x - \sin x} \) (l) \( y = \cos^3 \theta \) (m) \( y = \sin \left( \tan e^{5 \sin x} \right) \) (n) \( y = x^{x^2 \cos^{-2} x} \) (o) \( y = \left( \frac{\sin \theta}{1 + \cos \theta} \right)^2 \) (p) \( y = \sec \sqrt{x} \tan \left( \frac{1}{x} \right) \) (q) \( y = \frac{\cos x - \sin x}{\sin x} \) (r) \( y = \frac{2}{\csc x} + \frac{3}{\cos x} \) These equations represent functions that need to be differentiated with respect to their variables. Differentiation is a fundamental concept in calculus used to determine the rate at which a function is changing at any given point.
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Step 1: Given Information and Formula

According to Bartleby guidelines we are supposed to do the first three sub parts of multiple sub parts 

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Differential Formula 

fraction numerator d blank over denominator d x end fraction x to the power of n space equals space n x to the power of n minus 1 end exponent


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