Grade 11 Exam > Grade 11 Videos > Mathematics for Grade 11 > Derivative of Trigonometric Functions
Derivative of Trigonometric Functions Video Lecture | Mathematics for Grade 11
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FAQs on Derivative of Trigonometric Functions Video Lecture - Mathematics for Grade 11
| 1. What is the derivative of the sine function? |  |
Ans. The derivative of the sine function, denoted as d/dx(sin(x)), is equal to the cosine function, or cos(x). In other words, the rate of change of the sine function at any given point is given by the cosine function.
| 2. What is the derivative of the cosine function? | |
Ans. The derivative of the cosine function, denoted as d/dx(cos(x)), is equal to the negative sine function, or -sin(x). This means that the rate of change of the cosine function at any given point is given by the negative sine function.
| 3. How do you differentiate the tangent function? | |
Ans. To differentiate the tangent function, we use the quotient rule. The derivative of the tangent function, denoted as d/dx(tan(x)), is equal to sec^2(x), where sec(x) represents the secant function. Therefore, the rate of change of the tangent function at any given point is given by the secant squared function.
| 4. What is the derivative of the cotangent function? | |
Ans. The derivative of the cotangent function, denoted as d/dx(cot(x)), can be obtained by differentiating the reciprocal of the tangent function. Using the quotient rule, we find that the derivative of the cotangent function is equal to -csc^2(x), where csc(x) represents the cosecant function. Hence, the rate of change of the cotangent function at any given point is given by the negative cosecant squared function.
| 5. How do you find the derivative of the secant function? | |
Ans. To find the derivative of the secant function, denoted as d/dx(sec(x)), we can use the product rule in combination with the chain rule. The derivative is given by d/dx(sec(x)) = sec(x)tan(x). This means that the rate of change of the secant function at any given point is equal to the secant function multiplied by the tangent function.
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Dec 23, 2024 Last updated |
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