Question

Differentiate the following with respect to \( x \) i. \[ 3 x y^{2}+5 x+y^{2}+\frac{y}{x^{2}}=0 \] ii. \[ y=\frac{(x+2)^{2}(x-3)}{(\sqrt{2 x+5})(2 x+7)^{4}} \] \[ y=x^{x} \] iii. b. Find the limits of the following i. \[ \lim _{x \rightarrow \infty} \frac{5 x^{3}-4 x^{2}+5 x+2}{x^{3}-10} \] ii. \[ \lim _{x \rightarrow 1} \frac{\sqrt{x+5}-3}{x-4} \]

          Differentiate the following with respect to \( x \)
i.
\[
3 x y^{2}+5 x+y^{2}+\frac{y}{x^{2}}=0
\]
ii.
\[
y=\frac{(x+2)^{2}(x-3)}{(\sqrt{2 x+5})(2 x+7)^{4}}
\]
\[
y=x^{x}
\]
iii.
b. Find the limits of the following
i.
\[
\lim _{x \rightarrow \infty} \frac{5 x^{3}-4 x^{2}+5 x+2}{x^{3}-10}
\]
ii.
\[
\lim _{x \rightarrow 1} \frac{\sqrt{x+5}-3}{x-4}
\]

Differentiate the following with respect to x
i.

3 x y^2+5 x+y^2+(y)/(x^2)=0

ii.

y=((x+2)^2(x-3))/((√(2 x+5))(2 x+7)^4)

y=x^x

iii.
b. Find the limits of the following
i.

limx →∞(5 x^3-4 x^2+5 x+2)/(x^3-10)

ii.

limx → 1(√(x+5)-3)/(x-4)

Added by Richard E.

Calculus: Early Transcendentals

James Stewart 8th Edition

Chapter 3

Instant Answer

Solved by Expert Mary Wakumoto

05/20/2022

Step 1

\[ 3xy^2 + 5x + y^2 + \frac{y}{x^2} = 0 \] To differentiate implicitly with respect to \( x \): 1. Differentiate each term with respect to \( x \): \[ \frac{d}{dx}(3xy^2) + \frac{d}{dx}(5x) + \frac{d}{dx}(y^2) + \frac{d}{dx}\left(\frac{y}{x^2}\right) = 0 Show more…

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Differentiate the following with respect to \( x \) i. \[ 3 x y^{2}+5 x+y^{2}+\frac{y}{x^{2}}=0 \] ii. \[ y=\frac{(x+2)^{2}(x-3)}{(\sqrt{2 x+5})(2 x+7)^{4}} \] \[ y=x^{x} \] iii. b. Find the limits of the following i. \[ \lim _{x \rightarrow \infty} \frac{5 x^{3}-4 x^{2}+5 x+2}{x^{3}-10} \] ii. \[ \lim _{x \rightarrow 1} \frac{\sqrt{x+5}-3}{x-4} \]