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Derivative of Sum of Two Functions
Let y = u + v, where u and v are differentiable functions of x. or (u + v)' = u' + ..
Note 2:
If f and g are two continuous functions then f + g, f - g, fg are continuous function..
Step 2:
f ' (x) = (x - 6) (x - 4) + (x - 4) (x - 8) + (x - 6) (x - 8) f '(x)= (x 2 -10x + 24) + (x 2 - 12x + 32)+ (x 2 - 14x + 48) = 3x 2 - 36x + 104 f '(x) is defined for all values on the interval (4,10). \ f '(x) is differentiabl..
Example 2:
Differentiate the following function using product rule. y = (3 sec x - 4 cosec x) (2 sin x + 5 cos..
Step 2:
Find f '(x) and examine if it is defined at every point on the open interval (a, b). If f '(x) is defined for all x (a, b), then the function is differentiabl..
Step 2:
Solve f '(x) = 0 to get the critical values for f (x). Let these values be a, b, c. These are the points of maxima or minima. Arrange these values in ascending ord..
Seep 2:
Take the end points of the interva..
Step 2:
Differentiate f (x) and examine if f '(x) is defined at every point in the open interval (a, b..
Example 2:
The decay rate of radium at any point t is proportional to its mass at that time. The mass is M 0 at time t = 0. Form the differential equation and find the time when the mass will be halve..
Step 2:
Differentiate the terms containing x, y or both xy with respect to x. While differentiating the terms containing y or power of y, first..
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