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Exercise 1. Evaluate the followings derivatives a) and integrals b) a) $y = 3x^5, y = e^{\frac{1}{x}} \sin x, y = \frac{x}{\ln (2x)}$ b) $\int 2x dx, \int x\sqrt{1 - x^2} dx, \int x^2 \ln x dx,$

Name: exercise 1 evaluate the followings derivatives a and integrals b a y 3x5 y efrac1x sin x y fracxln 2x b int 2x dx int xsqrt1 x2 dx int x2 ln x dx 71004
Uploaded: 2024-04-11T03:28:59-08:00
Duration: 1 min 57 s
Channel: Keondre Parker
Description: exercise 1 evaluate the followings derivatives a and integrals b a y 3x5 y efrac1x sin x y fracxln 2x b int 2x dx int xsqrt1 x2 dx int x2 ln x dx 71004

          Exercise 1. Evaluate the followings derivatives a) and integrals b)
a) $y = 3x^5, y = e^{\frac{1}{x}} \sin x, y = \frac{x}{\ln (2x)}$
b) $\int 2x dx, \int x\sqrt{1 - x^2} dx, \int x^2 \ln x dx,$

$exercise 1 evaluate the followings derivatives a and integrals b a y 3x5 y efrac1x sin x y fracxln 2x b int 2x dx int xsqrt1 x2 dx int x2 ln x dx 71004$

Added by Francisco Jose S.

Calculus: Early Transcendentals

James Stewart 8th Edition

Instant Answer

Solved by Expert Keondre Parker

04/11/2024

Step 1

For the first function, $y = 3x^5$: We use the power rule for differentiation, which states that $\frac{d}{dx}(cx^n) = cnx^{n-1}$. Here, $c=3$ and $n=5$. $\frac{dy}{dx} = 3 \cdot 5x^{5-1} = 15x^4$. Show more…

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Exercise 1. Evaluate the followings derivatives a) and integrals b) a) $y = 3x^5, y = e^{\frac{1}{x}} \sin x, y = \frac{x}{\ln (2x)}$ b) $\int 2x dx, \int x\sqrt{1 - x^2} dx, \int x^2 \ln x dx,$