18) Differentiate (2x + 5) (3x + 7)-1 by using product rule, and quotient rule respectively Verify that the - Maths - Limits and Derivatives

Question

18) Differentiate (2x + 5) (3x + 7)-1 by using product
rule, and quotient rule respectively Verify that the answers
obtained are the same

Manbar Singh · Accepted Answer

PRODUCT RULE :Let y = 2x+53x+7-1⇒dydx = 2x+5×ddx3x+7-1 + 3x+7-1×ddx2x+5⇒dydx = 2x+5×-33x+72 + 13x+7×2⇒dydx = -32x+53x+72 + 23x+7⇒dydx =-32x+5 + 23x+73x+72⇒dydx = -6x - 15 + 6x + 143x+72⇒dydx = -13x+72QUOTIENT RULE :Let y = 2x+53x+7-1⇒y = 2x + 53x + 7⇒dydx = 3x+7×ddx2x+5 - 2x+5×ddx3x+73x+72⇒dydx = 3x+7×2 - 2x + 5×33x+72⇒dydx = 6x + 14 - 6x - 153x+72⇒dydx = -13x+72

18) Differentiate (2x + 5) (3x + 7)-1 by using product rule, and quotient rule respectively. Verify that the answers obtained are the same.

18) Differentiate (2x + 5) (3x + 7)^-1 by using product rule, and quotient rule respectively. Verify that the answers obtained are the same.