What are the differentiation formulas for finding the derivative of trigonometric functions?
Derivatives of Trigonometric Functions
| Function | Derivative |
|---|---|
| arccosx = cos-1x | -1/√(1-x2) |
| arctanx = tan-1x | 1/(1+x2) |
| arccotx = cot-1x | -1/(1+x2) |
| arcsecx = sec-1x | 1/(|x|∙√(x2-1)) |
Is the derivative of an exponential function is a logarithmic function?
Derivatives of exponential functions involve the natural logarithm function, which itself is an important limit in Calculus, as well as the initial exponential function. The derivative is the natural logarithm of the base times the original function.
What is the derivative of trigonometric function?
For example, the derivative of the sine function is written sin′(a) = cos(a), meaning that the rate of change of sin(x) at a particular angle x = a is given by the cosine of that angle.
Is the derivative of an exponential function another exponential function?
The derivative of an exponential function can be derived using the definition of the derivative. Derivatives of exponential functions involve the natural logarithm function, which itself is an important limit in Calculus, as well as the initial exponential function.
How to calculate the derivative of a logarithmic function?
Multiply by the natural log of the base. Multiply by the derivative of the exponent. So, now we’re going to learn the steps for differentiating logarithmic functions: Take the derivative of the function. Divide by the product of the natural log of the base and the rewritten function.
Is the derivative of log 2 6 a constant?
The first term, log 2 6, is a constant, so its derivative is 0. The term on the top, log 2 e, is a constant. If we need a decimal value, we can work it out using change of base as follows:
Is the differentiation of log based on the chain rule?
Derivatives of logarithmic functions are mainly based on the chain rule. However, we can generalize it for any differentiable function with a logarithmic function. The differentiation of log is only under the base
Is the differentiation of log under any base?
The differentiation of log is only under the base e, e, but we can differentiate under other bases, too. Now we will prove this from first principles: . x = 2 x = 2.
