Leibnitz's Theorem | Leibnitz Derivative Rule

You can find the Leibnitz derivative theorem below. We wish you good lessons...

Read More

Product Rule & Quotient Rule & Chain Rule (Derivative)

You can find the product rule, quotient rule and chain rule in the derivative below. We wish you good lessons.

Product Rule:

$\frac{d}{dx}(u(x).v(x))=u(x)\frac{dv}{dx}+v(x)\frac{du}{dx}$

Quotient Rule:

$\frac{d}{dx}(\frac{u(x)}{v(x)})=\frac{v(x)\frac{du}{dx}-u(x)\frac{dv}{dx}}{[v(x)]^2}$

Chain Rule:

$\frac{d}{dx}(f(g(x)))=f'(g(x))×g'(x)$

Read More

Laplace Transforms | Function and Transform (Examples)

You can find Laplace transforms below. We wish everyone good work.

You can find sample solutions below.

Read More

General Rules of Differantiation

In the following, u, v, w are functions of x; a, b, c, n are constants [restricted if indicated]; e=2.71828... is the natural base of logarithms; In u is the natural loraithm of u [i.e. the loraithm to the base e] where it is assumed thad u>0 and all angles are in radians.

Read More

Graphs of Hyperbolic Functions (Sinhx, Coshx, Tanhx, Cothx Graphics)

y=sinh x graph:

y=cosh x graph:

y=tanh x graph:

y=coth x graph:

y=sech x graph:

y=csch x graph:

Read More

Expression of Hyperbolic Functions In Terms of Others (Table)

 In the following we assume x>0.

Read More

$sec^{-1} x^2$ Derivative | What is derivative of sec x^2?

Hello everyone. You can reach derivative of $sec^{-1} x^2$ in this lesson. We wish you good work.

sec -1 derivative

What is derivative of $sec^{-1} x^2$?

$Sec^{-1} u$ derivative formulas:

$\frac{d}{dx}sec^{-1} u=\frac{1}{|u|.\sqrt{u^2-1}}.\frac{du}{dx}$

Now let's answer our question.

Differentiate $y=sec^{-1} x^2$

Solution For $x^2$ > 1 > 0,

>>> $\frac{dy}{dx}=\frac{1}{|x|\sqrt{(x^2)^2-1}}.\frac{d}{dx}x^2$

>>> $=\frac{2x}{x^2\sqrt{x^4-1}}=\frac{2}{x.\sqrt{x^4-1}}$

Answer = $\frac{2}{x.\sqrt{x^4-1}}$

Read More