Are trig functions differentiable?
We can use the definition of the derivative to compute the derivatives of the elementary trig functions. Theorem The function sin x is differentiable everywhere, and its derivative is cos x.
What is the derivative of cos?
-sin x
The derivative of the cosine function is written as (cos x)’ = -sin x, that is, the derivative of cos x is -sin x. In other words, the rate of change of cos x at a particular angle is given by -sin x.
What’s the derivative of sin2x?
2 cos 2x
The derivative of sin 2x is 2 cos 2x.
What is the derivative of sinx?
cos x
The derivative of sin x is denoted by d/dx (sin x) = cos x. The other way to represent the sine function is (sin x)’ = cos x.
What is the derivative of sin2x?
What is the derivative of cos2x?
Solution: Derivative of cos 2x is -2 sin 2x.
What is the derivative of cos 3x?
-3 sin3x
The derivative of cos3x is equal to -3 sin3x. The derivative of a function gives the rate of change in that function with respect to the change in the variable. We can calculate the derivative of cos3x using different methods of differentiation such as the chain rule and first principle of derivatives.
What are the basic laws of derivative?
Power Rule: If xn is the function, then the derivative is nxn-1. Quotient Rule: If the function is f/g, then the derivative is [f’g-g’f]/g2. Reciprocal Rule: If the function is 1/f, then the derivative is -f’/f2. Chain Rule: If f⚬g is the function, then the derivative of the function is (f’ ⚬ g) x g’.
What is the 4 step rule in derivatives?
The following is a four-step process to compute f/(x) by definition. Input: a function f(x) Step 1 Write f(x + h) and f(x). Step 2 Compute f(x + h) – f(x). Combine like terms.
What are the four basic rules of derivatives?
Where do we use derivatives in real life?
Application of Derivatives in Real Life
- To calculate the profit and loss in business using graphs.
- To check the temperature variation.
- To determine the speed or distance covered such as miles per hour, kilometre per hour etc.
- Derivatives are used to derive many equations in Physics.