Find the Derivative - d/dx (-3x)/y

Problem

d()/d(x)(−3*x)/y

Solution

1. Identify the rule needed for differentiation. Since the expression is a quotient of two functions where y is assumed to be a function of x we must use the quotient rule: d()/d(x)u/v=(vd(u)/d(x)−ud(v)/d(x))/(v2)

2. Assign the variables for the quotient rule. Let u=−3*x and v=y

3. Differentiate the numerator and denominator with respect to x

(d(−)*3*x)/d(x)=−3

d(y)/d(x)=d(y)/d(x)

4. Apply the quotient rule formula by substituting the derivatives back into the expression.

(y*(−3)−(−3*x)d(y)/d(x))/(y2)

5. Simplify the numerator by performing the multiplication and handling the signs.

(−3*y+3*xd(y)/d(x))/(y2)

Final Answer

d()/d(x)(−3*x)/y=(3*xd(y)/d(x)−3*y)/(y2)

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