Find the Derivative - d/dx -x/(4y)

Problem

d()/d(x)*(−x/(4*y))

Solution

1. Identify the variable of differentiation as x and treat y as a function of x which requires the use of the quotient rule or the product rule with implicit differentiation.

2. Apply the quotient rule formula d()/d(x)u/v=(vd(u)/d(x)−ud(v)/d(x))/(v2) where u=−x and v=4*y

3. Differentiate the numerator and denominator with respect to x

(d(−)*x)/d(x)=−1

(d(4)*y)/d(x)=4d(y)/d(x)

4. Substitute these derivatives back into the quotient rule formula.

(4*y*(−1)−(−x)*(4d(y)/d(x)))/((4*y)2)

5. Simplify the expression by performing the multiplication and squaring the denominator.

(−4*y+4*xd(y)/d(x))/(16*y2)

6. Factor out the common factor of 4 in the numerator to simplify the fraction.

(4*(−y+xd(y)/d(x)))/(16*y2)

7. Reduce the fraction by dividing both the numerator and denominator by 4

(−y+xd(y)/d(x))/(4*y2)

Final Answer

d()/d(x)*(−x/(4*y))=(xd(y)/d(x)−y)/(4*y2)

Want more problems? Check here!