The tangent of x is defined as sine of x divided by cosine of x.
tanx = ˢⁱⁿˣ⁄cₒsₓ
Since tanx can be written as sinx divided by cosx, we can find the derivative of tanx using quotient rule.
Consider a function defined by y as shown below.
y = ᵘ⁄ᵥ
Let u and v be the functions of x.
Then the derivative of y with respect to x :
The above formula is called the Quotient Rule of Derivative.
Derivative of Tanx :
Substitute tanx for y, sinx for u and cosx for v into the above formula and and find the derivative of tanx.
Therefore, the derivative of tangent of x is sec2x.
Find the derivative of each of the following.
Problem 1 :
We already know the derivative of tanx, which is sec2x. We can find the derivative of tan(3x) using chain rule.
Problem 2 :
tan(5x - 6)
= [tan(5x - 6)]'
= [sec2(5x - 6)](5x - 6)'
= [sec2(5x - 6)](5)
= 5sec2(5x - 6)
Problem 3 :
tan(2x2 - 3x + 1)
= [tan(2x2 - 3x + 1)]'
= [sec2(2x2 - 3x + 1)](2x2 - 3x + 1)'
= [sec2(2x2 - 3x + 1)](4x - 3)
= (4x - 3)sec2(2x2 - 3x + 1)
Problem 4 :
Problem 5 :
Problem 6 :
Problem 7 :
Problem 8 :
Kindly mail your feedback to email@example.com
We always appreciate your feedback.
©All rights reserved. onlinemath4all.com
May 26, 23 12:27 PM
May 21, 23 07:40 PM
May 20, 23 10:53 PM