I need help with problem 7.2.2 D as well as G METHODS OF DIFFERENTIATATION124Let e= (r + 1)!/2, Thendydrdv1.drpowerdv%3D-1/2x 2x =rule,drThereforedy(62 v²-(23-5)r)/v3%3Ddr= (6z(r +1) – 2a³ + 5)(4ar3 + 6x + 5)x(r2 + 1)3/2Two final points about the rules1. There is often more than one way of differentiating a particular function: thus inExample 1 we could use the quotient rule instead of the composite function rule.2. It often saves time to simplify before differentiating; in particular, this avoidsunnecessary use of the product and quotient rules. For example, the functiony = (52 + 2r)r² could be differentiated using the product rule but it is mucheasier to write y = 5x*+2x³ and then differentiate: dy/dx = 20x3+6x². Similarly,the function y = (5x² + 2x)/x² should not be differentiated by the quotient rule;instead, we write y = 5+2x¬1, and the derivative is easily seen to be -2/x².Exercises7.2.1 The functions f and g are defined as follows:f(x) = a° +1, g(x) = x* – 2.Find expressions for f(g(x)), g(f(x)) and their derivatives.7.2.2 Differentiate:(a) (3z–7)10 (b) (³ + 1)% (c) (4x+9)'/2 (d) (2° – 1)2/3 (e) (a/4+5)6(Đ ( - 3ar + 5a + 1)/4 (8) 1/(x² – 1)* (h) 8/(V+2)57.2.3 Differentiate using the rules of this and the previous section:(a) (2² – 1)(2³ + 1)°, (b) (/3 - 2)/(2 - 2)3.

Question

I need help with problem 7.2.2   D as well as G METHODS OF DIFFERENTIATATION124Let e= (r + 1)!/2, Thendydrdv1.drpowerdv%3D-1/2x 2x =rule,drThereforedy(62 v²-(23-5)r)/v3%3Ddr= (6z(r +1) – 2a³ + 5)(4ar3 + 6x + 5)x(r2 + 1)3/2Two final points about the rules1. There is often more than one way of differentiating a particular function: thus inExample 1 we could use the quotient rule instead of the composite function rule.2. It often saves time to simplify before differentiating; in particular, this avoidsunnecessary use of the product and quotient rules. For example, the functiony = (52 + 2r)r² could be differentiated using the product rule but it is mucheasier to write y = 5x*+2x³ and then differentiate: dy/dx = 20x3+6x². Similarly,the function y = (5x² + 2x)/x² should not be differentiated by the quotient rule;instead, we write y = 5+2x¬1, and the derivative is easily seen to be -2/x².Exercises7.2.1 The functions f and g are defined as follows:f(x) = a° +1, g(x) = x* – 2.Find expressions for f(g(x)), g(f(x)) and their derivatives.7.2.2 Differentiate:(a) (3z–7)10 (b) (³ + 1)% (c) (4x+9)'/2 (d) (2° – 1)2/3 (e) (a/4+5)6(Đ ( - 3ar + 5a + 1)/4 (8) 1/(x² – 1)* (h) 8/(V+2)57.2.3 Differentiate using the rules of this and the previous section:(a) (2² – 1)(2³ + 1)°, (b) (/3 - 2)/(2 - 2)3.

Accepted Answer

(d)
The given function is y=x6-123.
Evaluate the derivative of the given function as follows.…