I am having trouble simplifying this expression. Can someone show me step by step?
y′ = 4(5x − 1)^3(5)(7x^2 − 1)^−3 + (5x − 1)^4(−3)(7x^2 − 1)^−4(14x)
y'= 20(5x − 1)^3(7x^2 − 1)^−3 − 42x(5x − 1)^4(7x^2 − 1)^−4
az_lender
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Some further symbols of inclusion would've been helpful; I'll assume you mean:
y' = (20)[(5x-1)^3][(7x^2-1)^(-3)] - (42x)[(5x-1)^4][(7x^2-1)^(-4)].
I would rewrite it as:
y' = [(5x-1)^3][(7x^2-1)^(-4)] [(20)(7x^2-1) - (42x)(5x-1)]
= [(5x-1)^3] [(7x^2-1)^(-4)] [140x^2 - 20 - 210x^2 + 42x]
= [(42x - 20 - 70x^2)(7x^2 - 1)^4 ] / [(5x-1)^3],
and I wouldn't try to go any farther than that.
The first trinomial may be factorable,
but its factors won't "cancel" anything.