Discover The Power Of The Reciprocal Rule: Calculus Derivatives Made Easy

Reciprocal Rule

Function 1/fDerivative −f’/f2

The reciprocal rule in calculus refers to the relationship between the derivative of a function and the reciprocal of the function. This rule states that:

– If y = f(x) is a differentiable function with f(x) ≠ 0, then the derivative of 1/f(x) is given by:

(1/f(x))’ = -f'(x) / (f(x))^2

In other words, the derivative of the reciprocal of a function is equal to the negative of the derivative of the function divided by the square of the function.

The reciprocal rule can be used to find derivatives of functions involving fractions or ratios. For example, if we want to find the derivative of y = 1/(x+1), we can first rewrite it as y = (x+1)^(-1) and then use the reciprocal rule to obtain:

y’ = -1*(x+1)^(-2)*(1) = -1/(x+1)^2

This tells us that the slope of the tangent line to the curve y = 1/(x+1) at any point (x,y) is given by -1/(x+1)^2.

Overall, the reciprocal rule is a useful tool for finding derivatives of functions involving fractions or ratios, and can be applied in various contexts in calculus and other areas of mathematics.

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