## ddx tanx

### To find the derivative of the tangent function, we can use the quotient rule

To find the derivative of the tangent function, we can use the quotient rule. The derivative of tan(x) can be expressed as:

ddx tanx = ddx (sinx/cosx)

Let’s denote u = sinx and v = cosx. Applying the quotient rule, we have:

ddx (sinx/cosx) = (v du/dx – u dv/dx) / (v^2)

Now, let’s find the derivatives of u and v:

du/dx = d/dx (sinx) = cosx

dv/dx = d/dx (cosx) = -sinx

Substituting these values into the quotient rule formula, we get:

ddx (sinx/cosx) = (cosx * cosx – sinx * (-sinx)) / (cosx)^2

Simplifying further:

ddx (sinx/cosx) = (cos^2(x) + sin^2(x)) / (cos^2(x))

= 1 / cos^2(x)

Since tan(x) is defined as sinx/cosx, we can rewrite this result as:

ddx tanx = 1 / cos^2(x)

So, the derivative of the tangent function is 1 divided by the square of the cosine of x, expressed as 1 / cos^2(x).

## More Answers:

Finding the Value of cos^-1(1): Understanding the Inverse Cosine Function and its Angle RepresentationUnderstanding the Chain Rule: Finding the Derivative of sin(x)

Understanding the Chain Rule: Derivative of cos(x) with Respect to x is -sin(x)