calculus derivative product rule

'Derivative of the product of two functions = first function x derivative of second function + second function x derivative of first function..

Let y = u. v, where both u and v are differentiable functions of x.Let y = u. v, where both u and v are differentiable functions of x. or (u.v)' = u.v' + v .u' It can be remembered ..

Derivative of a Function of a Function - So far, we know how to differentiate functions like sin x and x 3 - 5. But how do we differentiate a function of a function? That is how can we differentiate sin (x 3 - 5)?So far, we know how to differentiate functions like sin x and x 3 - 5. But h..

Quotient Rule for Differentiation - In this section, we derive the formulaIn this section, we derive the formula and use it to differentiate quotients of function..

Differentiate the following function using product rule. y = (3 sec x - 4 cosec x) (2 sin x + 5 cos..

If we divide by uv in the formula ((u.v)' = u.v' + v .u'), we have It can be generalised for derivative of the product of more than two functions as given below:..

A first-order differential equation is said to be linear if, in it, the unknown function y and its derivative y' appear with non-negative integral index not greater than one and not as product yy' either. Hence, a first-order linear differential equation is of the form: where..

So far we have discussed the derivative of a function f(x) at a point 'a' which is in the domain of f. Suppose we want to find the derivative of the same function at a different point 'b', then we have to compute the derivative by repeating the same process. To avoid t..