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How To Use Quotient Rule To Compute Derivatives

Th quotient rule is the rule to compute the derivative of the ratio of two functions. It says that

$\displaystyle \frac{d}{dx }\left(\frac{f}{g}\right)=\frac{\frac{df}{dx}g-f\frac{dg}{dx}}{g^2}$ .

Sometimes it is easier to memorize as

$\displaystyle \left(\frac{f}{g}\right)'=\frac{f'g-fg'}{g^2}$ .

The first video below is a song about quotient rule that will make you easier to memorize this rule. The others, will give you examples how to use this rule.

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How To Use Product Rule To Compute Derivatives

The product rule is the rule that enable us to compute the derivative of a product of two functions without simplifying the product first. It states that

$\frac{d}{dx}(fg)=\frac{df}{dx}g+f\frac{dg}{dx}$

Some people feel that memorizing the rule in the form

$(fg)'=f'g+fg'$ or $(uv)'=u'v+uv'$ are easier. The videos below will guide you to use this rule to find the derivatives of a product of two functions.

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How To Solve Equations With Radicals

The first step to solve radical equation is to isolate the radical on the left hand side of the equation. After that think of an operation that can eliminate the radical notation. Let see some simple example.

Solve $\sqrt{x+5}+2=4$

Add $-2$ to both sides to eliminate the 2 from the left to get $\sqrt{x+5}=4$ . Now the operation that can eliminate the square root is squaring. So squaring both sides, we have $x+5= 4$ . Hence $x=-1$ . Now we need to check that this result is really a solution by plugin back to the original equation. For this problem one can easily check that $x=-1$ is a solution.

Why we need to plugin back the final result to the original equation? The reason of this is that the process of squaring (or raising to even power) doesn't give us an equivalent equation. To illustrate this onsider $x=5$ if we square both sides we have $x^2=25$ . But the last equation has two solutions $x=\pm 5$ .

The videos below will give you examples how to solve many kind of equations with radicals.

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How To Use Quotient Rule To Compute Derivatives

How To Use Product Rule To Compute Derivatives

How To Solve Equations With Radicals