Derivative measures the rate of change in one variable with respect to the change in the other variable.
For example, let x be an independent variable and y be a dependent variable.
So, the value of y is getting changed according to the change in the value of x.
Then, the derivative of y with respect to x is
dy/dx
Power rule of derivative is the fundamental tool to find the derivative of a function in the form
y = xn
To get the derivative of xn with respect to x, we have to bring the exponent n in front of x and subtract 1 from the exponent.
dy/dx = nxn - 1
Example 1 :
y = x3
dy/dx = 3x3 - 1
= 3x2
Example 2 :
y = x2.
dy/dx = 2x2 - 1
= 2x1
= 2x
We can find the derivative of x with respect to x using the power rule of derivative.
y = x
y = x1
Use the power rule of derivative.
dy/dx = 1x1 - 1
= 1x0
= 1(1)
= 1
So, the derivative of x with respect to x is 1.
We can extend this concept to any variable like y or t.
Derivative of y with respect to y is 1.
Derivative of t with respect to t is 1.
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