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# Differentiation Rules

Chain Rule Inverse Function Linearity , where c is a constant Product Rule Quotient Rule Reciprocal Rule Differentiation of Implicit Functions
If an equation is expressed as y = f(x), then y is said to be the explicit function of x. However if y is connected with x by an expression f (x, y) = 0, then y is said to an implicit function of x. For e.g. x2 + 3xy + y2 = 0.

For differentiating the implicit function we differentiate each term with respect to x keeping in mind that if there is a term contains powers of y, we differentiate first with respect to y and then multiply it by
dy/dx to get its differentiation with respect to x.

Example 1: Example 2: Calculate dy/dx for x3-3y2=21
Differentiating both side of equation with respect to x, and using The Sum Rule: Now using The Chain Rule which leads to: Example 3: Differentiate  Recall that D{ax} = axlna Recall that axax = ax+x = a2x and axbx = (ab)x Recall that lnA – lnB = ln(A/B) Example 4: Differentiate  Factor 2x and (x2 – 1)2 from the numerator Web-Formulas.com © 2023 | Contact us | Terms of Use | Privacy Policy |  