For which value of a does the expression d/dx (axb) = 5bxa-1 hold true if b does not equal to 0?

Question

For which value of a does the expression d/dx (ax^b) = 5bx^a-1 hold true if b does not equal to 0?

a)5

b)3

c)9

d)7

Answer 1

d/dx(ax^b) = abx^b-1

abx^b-1 = 5bx^a-1 when ab = 5b and b-1 = a-1.

Since b is not zero, we get a = 5 and b = 5.