Question

3 Use the product rule to differentiate each function with respect to $x$. a $y = x^2(3x + 1)^2$ c $y = x^2(4x + 1)^3$ e $y = (2x + 3)^5(3x - 4)^4$ i $y = \sqrt{x + 3}(x^2 - 3x)$ k $y = \sqrt{x^2 + 1}(2x + 1)^3$ b $y = (x^2 + 1)(3x + 1)$ d $y = (x^2 - 1)(x^3 + 2x + 3)$ f $y = (x^2 + 3x + 4)^4(2x + 3)^3$ h $y = (3x^2 - 4x + 5)^2(x^2 + 1)$ j $y = (2x - 5)^\frac{3}{2}(3x + 4)^2$ l $y = (x + 1)^3(x^2 - 1)^2$

          3 Use the product rule to differentiate each function with respect to $x$.
a $y = x^2(3x + 1)^2$
c $y = x^2(4x + 1)^3$
e $y = (2x + 3)^5(3x - 4)^4$
i $y = \sqrt{x + 3}(x^2 - 3x)$
k $y = \sqrt{x^2 + 1}(2x + 1)^3$
b $y = (x^2 + 1)(3x + 1)$
d $y = (x^2 - 1)(x^3 + 2x + 3)$
f $y = (x^2 + 3x + 4)^4(2x + 3)^3$
h $y = (3x^2 - 4x + 5)^2(x^2 + 1)$
j $y = (2x - 5)^\frac{3}{2}(3x + 4)^2$
l $y = (x + 1)^3(x^2 - 1)^2$

3 Use the product rule to differentiate each function with respect to x.
a y = x^2(3x + 1)^2
c y = x^2(4x + 1)^3
e y = (2x + 3)^5(3x - 4)^4
i y = √(x + 3)(x^2 - 3x)
k y = √(x^2 + 1)(2x + 1)^3
b y = (x^2 + 1)(3x + 1)
d y = (x^2 - 1)(x^3 + 2x + 3)
f y = (x^2 + 3x + 4)^4(2x + 3)^3
h y = (3x^2 - 4x + 5)^2(x^2 + 1)
j y = (2x - 5)^(3)/(2)(3x + 4)^2
l y = (x + 1)^3(x^2 - 1)^2

Added by Erica S.

Calculus: Early Transcendentals

James Stewart 8th Edition

Instant Answer

Solved by Expert Madhur L

06/17/2022

Step 1

Let's label the two factors as u and v, where u = x^3 and v = x+1. Using the product rule, the derivative of ay with respect to x is given by: ay' = u'v + uv' Show more…

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Use the product rule to differentiate each function with respect to x. Questions i, j, k, l. please 3 Use the product rule to differentiate each function with respect to x ay=x3x+1 by=x+13x+1 cy=x2(4x+13 dy=x-1x+2x+3 ey=(2x+3)3x-44 fy=(x+3x+42x+33 3n-1)4 hy=3x-4x+5x+1 i y=x+3(x-3x) j y=2x-53x+42 ky=x+12x+1 1y=x+13x-12