If Y = 21X^1/3(25 + X⁴),then dY/dX is: A) 7X^-2/3(25 + X⁴) + 84X^10/3. B) 7X^2/3(25 + X⁴) + 84X^10/3. C) 7X^-1/3(25 + X⁴) + 84X^10/3. D) 7X^1/3(25 + X⁴) + 84X^10/3. E) 7X^1/3(25 + X⁴).

Question

Quizplus · Accepted Answer

The product rule is used to differentiate the given function. The product rule states that if f(x) = g(x)h(x), then f'(x) = g'(x)h(x) + g(x)h'(x). In this case, g(x) = 21X^(1/3) and h(x) = 25 + X^4. Therefore, g'(x) = 7X^(-2/3) and h'(x) = 4X^3. Substituting these values into the product rule, we get:f'(x) = g'(x)h(x) + g(x)h'(x)= 7X^(-2/3)(25 + X^4) + 21X^(1/3)(4X^3)= 7X^(-2/3)(25 + X^4) + 84X^(10/3)

If Y = 21X1/3(25 + X4),then DY/dX Is

If Y = 21X^1/3(25 + X⁴),then DY/dX Is