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Example:
Solve the differential equation , ..
Solve the differential equation , ..Product Rule for Differentiation
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..
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..Proof:
Put a + b - x = t -dx = dt when x = a, t = b x = b, t = a = LHS Put a - x = t -dx = dt When x = 0, t = a x = a, t = 0 ..
Put a + b - x = t -dx = dt when x = a, t = b x = b, t = a = LHS Put a - x = t -dx = dt When x = 0, t = a x = a, t = 0 ..Examples:
Derivatives are also used to trace the graphs of different functions. To optimise the value of a differentiable function of practical use, derivatives of the functions are applied. This chapter reveals with many more application of derivatives such as determining the relative error in me..
Application of Derivatives Introduction
Introduction - Let us began this chapter with the following statement: Often a physician may want to test how small changes in dosage can affect the body's response to a particular drug. An economist may want to study how investment changes with variation in interest rates. How the velocity of a he..
Application of Derivatives Animation
Application of Derivatives Animation..
Application of Derivatives Animation..Theorem 1:
Let f be continuous on [a, b] and differentiable on the open interval (a, b). Then (a) f is increasing on [a, b] if f '(x) > 0 for each x (a, b) (b) f is decreasing on [a, b] if f '(x) < 0 for each x (a, b) This theorem can be proved by using Mean Value Theorem. We shall prove the theore..
Let f be continuous on [a, b] and differentiable on the open interval (a, b). Then (a) f is increasing on [a, b] if f '(x) > 0 for each x (a, b) (b) f is decreasing on [a, b] if f '(x) < 0 for each x (a, b) This theorem can be proved by using Mean Value Theorem. We shall prove the theore..First Fundamental Theorem of Integral Calculus
If f(x) is a continuous function on the closed interval [a, b], and if Area function is defined ..
If f(x) is a continuous function on the closed interval [a, b], and if Area function is defined ..Second Fundamental Theorem of Integral Calculus
If f (x) is a function continuous on [a, b] then ..
If f (x) is a function continuous on [a, b] then ..See what our Users say :
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