subject: Derivative Of X Sinx [print this page] Introduction to derivative: Introduction to derivative:
In mathematics, we study different topics. Derivative is one of the part mostly used in calculus. Derivative is also known as differentiation. Derivative is used for finding the rate of change of the function. The derivative of the function z is denoted as z'. Different variables and functions are used in derivatives. Different formulas are used for finding the derivative values.
Derivative formulas:
'(d)/(dx) (x^y) = yx^(y-1)'
'(d)/(dx) x = 1'
'(d)/(dx) (2) = 0'
'(d)/(dx) (uv) = u((dv)/(dx)) + v((du)/(dx))'
Example Problems for Derivative of X Sinx
Derivative example problem 1:
Find the first derivative value of the given function f(x) = x sinx.
Solution:
Given function is f(x) = x sinx
Using the formula, we differentiate the given function
'(d)/(dx) (uv) = u ((dv)/(dx)) + v ((du)/(dx))'
From the given function
u = x and v = sinx
Differentiate the above values with respect to x, we get
du = 1 dx and dv = cosx dx
Substitute the given values in the above formula, we get
'(d)/(dx) (uv)' = x (cosx) + sinx (1)
= xcosx + sinx
Answer:
The final answer is xcosx + sinx
Derivative example problem 2:
Find the first derivative value of the given function f(x) = 2x sinx.
Solution:
Given function is f(x) = 2x sinx
Using the formula, we differentiate the given function
'(d)/(dx) (uv) = u ((dv)/(dx)) + v ((du)/(dx))'
From the given function
u = 2x and v = sinx
Differentiate the above values with respect to x, we get
du = 2 dx and dv = cosx dx
Substitute the given values in the above formula, we get
' (d)/(dx) (uv)' = x (cosx) + sinx (2)
= xcosx + 2sinx
Answer:
The final answer is xcosx + 2sinx
Derivative Example Problem 3:
Find the first derivative value of the given function f(x) = x 3sinx.
Solution:
Given function is f(x) = x 3sinx
Using the formula, we differentiate the given function
'(d)/(dx) (uv) = u ((dv)/(dx)) + v ((du)/(dx))'
From the given function
u = x and v = 3sinx
Differentiate the above values with respect to x, we get
du = 1 dx and dv = 3cosx dx
Substitute the given values in the above formula, we get
