Find the Derivative - d/dx 4x-y=17

Problem

d()/d(x)*(4*x−y=17)

Solution

1. Identify the method of implicit differentiation, as the equation involves both x and y

2. Differentiate both sides of the equation with respect to x

3. Apply the sum rule and the constant rule to the left side.

(d(4)*x)/d(x)−d(y)/d(x)=d(17)/d(x)

4. Evaluate the derivatives, noting that the derivative of x is 1 the derivative of y is d(y)/d(x) and the derivative of a constant is 0

4−d(y)/d(x)=0

5. Isolate the term d(y)/d(x) by adding it to both sides of the equation.

4=d(y)/d(x)

Final Answer

d(y)/d(x)=4

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