Question

If y = 9x-4/5√x calculate dy/dx____

Answer 1

To calculate dy/dx for the given equation y = (9x - 4) / (5√x), you need to differentiate the equation with respect to x using the quotient rule. The derivative will be (26 - 18x) / x.

Step-by-step explanation:

To calculate dy/dx for the given equation y = (9x - 4) / (5√x), we need to differentiate the equation with respect to x using the quotient rule.

Let's break down the steps:

1. First, find the derivative of the numerator: d/dx (9x - 4) = 9
2. Next, find the derivative of the denominator: d/dx (√x) = (1/2)x^(-1/2)
3. Apply the Quotient Rule: dy/dx = (denominator * numerator - numerator * denominator) / (denominator^2)
4. Substitute the values obtained in steps 1 and 2 into the Quotient Rule: dy/dx = ((1/2)x^(-1/2)(9) - (9x - 4)(1/2)x^(-1/2)) / ((1/2)x^(-1/2))^2
5. Simplify the equation by multiplying and dividing through by (1/2)x^(-1/2) and simplifying the exponent: dy/dx = (9 - (9x - 4)) / (1/2)x

So, dy/dx = (9 - 9x + 4) / (1/2)x = (13 - 9x) / (1/2)x = (26 - 18x) / x.