tmt said:So, I have
$$\d{x}{t} = 20 sex^2∂ \d{∂}{t}$$
And the text goes to:
$$ \d{∂}{t} = \frac{1}{20}cos^2 ∂ \d{x}{t}$$
I don't understand where the cos comes from? Is it a trigonometric identity? If so I can't find it.
A trigonometric function is a mathematical function that relates the angles of a right triangle to the lengths of its sides. Common trigonometric functions include sine, cosine, tangent, and their inverse functions.
To differentiate a trigonometric function, you can use the chain rule or the product rule, depending on the specific function. First, identify the function and its derivative, then apply the appropriate rule to find the derivative of the function.
The derivative formulas for common trigonometric functions are:
Yes, you can differentiate inverse trigonometric functions using the inverse function theorem. This theorem states that the derivative of an inverse function is equal to the reciprocal of the derivative of the original function.
To find the slope of a curve at a specific point, you can evaluate the derivative of the trigonometric function at that point. The resulting value will be the slope of the curve at that point. This can be useful in calculating the instantaneous rate of change of a function at a given point.