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.

How do you implicitly differentiate a function?

How do I perform implicit differentiation? In implicit differentiation, we differentiate each side of an equation with two variables (usually x and y) by treating one of the variables as a function of the other. This calls for using the chain rule.

How do you do implicit differentiation with sin?

Implicit Differentiation to Determine the Derivative of sin(xy) To determine the derivative of y = sin(xy), we will use implicit differentiation by remembering that (d/dx)y = y’. First, apply the derivative to both sides of the equation: d/dx(y) = d/dx (sin(xy)).

What is explicit and implicit differential equation?

Implicit/Explicit Solution An explicit solution is any solution that is given in the form y=y(t) y = y ( t ) . In other words, the only place that y actually shows up is once on the left side and only raised to the first power. An implicit solution is any solution that isn’t in explicit form.

How do you differentiate 10x?

1 Answer. The derivative of 10x with respect to x is 10.

What is the difference between trigonometric function and hyperbolic function?

In mathematics, hyperbolic functions are analogues of the ordinary trigonometric functions, but defined using the hyperbola rather than the circle. Just as the points (cos t, sin t) form a circle with a unit radius, the points (cosh t, sinh t) form the right half of the unit hyperbola.

What is implicit differentiation formula?

Implicit differentiation is the process of differentiating an implicit function which is of the form f(x, y) = 0 and finding dy/dx. To find it, Differentiate both sides of f(x, y) = 0 with respect to x. Apply usual derivative formulas to differentiate the x terms.