How to use Derivative Calculator?

Here are step-by-step instructions on how to use the Derivative Calculator:

Step-1: Select the Derivative Order::

Locate the dropdown menu labeled “Select nth Derivative.”

Click on the dropdown menu and choose the order of the derivative you want to compute (from 1st to 10th derivative).

Step-2: Enter the Function:

Find the text input box labeled “Derivative of”

Click inside the text box and type your function. For example, if you want to differentiate \sin(x), type sin(x).

Step-3: Submit the Function:

After selecting the derivative order and entering your function, click the “Submit” button.

---

Derivative rules:

---

Examples of the derivative of the function.

 

Find the derivative of f(x)=3x^3-5x^2+6x−4

f(x)=3x^3-5x^2+6x−4

Take derivative.

f'(x)=\frac{d}{dx}\left(3x^3-5x^2+6x−4\right)\\

f'(x)=\frac{d}{dx}\left(3x^3\right)-\frac{d}{dx}\left(5x^2\right)+\frac{d}{dx}\left(6x\right)-\frac{d}{dx}\left(4\right)\\

f'(x)=9x^2-10x+6-0\\

f'(x)=9x^2-10x+6\\

---

 

Find the derivative of f(x)=\frac{x-1}{x-2}

f(x)=\frac{x-1}{x-2}

Take derivative.

f'(x)=\frac{d}{dx}\left(\frac{x-1}{x-2}\right)

Apply the quotient rule for the derivative: \left(\frac{f}{g}\right)'=\frac{f'\cdot g-g'\cdot f}{g^2}

f'(x)=\frac{\frac{d}{dx}\left(x-1\right)\left(x-2\right)-\frac{d}{dx}\left(x-2\right)\left(x-1\right)}{\left(x-2\right)^2}\\

f'(x)=\frac{1\cdot \left(x-2\right)-1\cdot \left(x-1\right)}{\left(x-2\right)^2}\\

f'(x)=\frac{x-2-\left(x-1\right)}{\left(x-2\right)^2}\\

f'(x)=\frac{x-2-x+1}{\left(x-2\right)^2}\\

f'(x)=\frac{-1}{\left(x-2\right)^2}\\

f'(x)=-\frac{1}{\left(x-2\right)^2}\\

---

 

Find the derivative of f(x)=x^2\sin \left(x\right)

f(x)=x^2\sin \left(x\right)

Take derivative.

f'(x)=\frac{d}{dx}\left(x^2\sin \left(x\right)\right)

Apply the product rule for the derivative: \left(\frac{f}{g}\right)'=\frac{f'\cdot g-g'\cdot f}{g^2}

f'(x)=\frac{d}{dx}\left(x^2\right)\sin \left(x\right)+\frac{d}{dx}\left(\sin \left(x\right)\right)x^2\\

f'(x)=2x\sin \left(x\right)+\cos \left(x\right)x^2\\

f'(x)=2x\sin \left(x\right)+x^2\cos \left(x\right)\\

---