Derivative calc is used to find the derivative of any function such as algebraic, exponential, trigonometric etc. Derivative simple means the differentiation of the function. Differentiation in terms of x is simply represented by d/dx, if derivative is with respect to x. This tool is also known as smart tool as it reads both 5x and 5 *x. Sometimes 5*x is represented simply 5x. So it reads such function as well and hence after recognising the function, it finds the required derivative of the function.
This can be more clarified by the examples mentioned below:-
Question 1: Find the derivative of function x = y^10 with respect to y.
Solution: Given x = y^10
Now d/dy (y^10)
= 10 y ^ (10-1) (because d/dx x^n = n x^ (n-1))
= 10 y ^ 9
So 10 y ^ 9 is the required derivative of function x = y^10 with respect to y.
Question 2: If d/dx (f(x)) = Cos x, then find the f(x) and also find d/dx Sin (2x).
Solution: Given d/dx (f(x)) = Cos x - equation 1
We know that, d/dx Sin x = Cos x - equation 2
Therefore by comparing the equation 1 and equation 2,
So the value of f(x) = Sin x.
Now we need to find d/dx Sin (2 x)
So d/dx Sin (2x)
= Cos 2x d/dx (2x)
= Cos 2 x. 2 = 2. Cos 2x
Therefore after differentiation, we find that d/dx Sin (2 x) = 2. Cos 2x