High School Math : Finding Derivatives

Example Questions

Example Question #4 : Derivative Defined As The Limit Of The Difference Quotient

Explanation:

To solve this equation, we can use the power rule. To use the power rule, we lower the exponent on the variable and multiply by that exponent.

We're going to treat  as  since anything to the zero power is one.

Notice that  since anything times zero is zero.

Example Question #5 : Derivative Defined As The Limit Of The Difference Quotient

What is the derivative of ?

Explanation:

To solve this equation, we can use the power rule. To use the power rule, we lower the exponent on the variable and multiply by that exponent.

We're going to treat  as  since anything to the zero power is one.

Notice that  since anything times zero is zero.

That leaves us with .

Simplify.

As stated earlier, anything to the zero power is one, leaving us with:

Example Question #6 : Derivative Defined As The Limit Of The Difference Quotient

What is the derivative of ?

Explanation:

To solve this equation, we can use the power rule. To use the power rule, we lower the exponent on the variable and multiply by that exponent.

We're going to treat  as  since anything to the zero power is one.

Notice that  since anything times zero is zero.

Just like it was mentioned earlier, anything to the zero power is one.

Example Question #7 : Derivative Defined As The Limit Of The Difference Quotient

What is the derivative of ?

Explanation:

To take the derivative of this equation, we can use the power rule. The power rule says that we lower the exponent of each variable by one and multiply that number by the original exponent.

Simplify.

Remember that anything to the zero power is equal to one.

Example Question #8 : Derivative Defined As The Limit Of The Difference Quotient

What is the derivative of ?

Explanation:

To take the derivative of this equation, we can use the power rule. The power rule says that we lower the exponent of each variable by one and multiply that number by the original exponent.

We are going to treat  as  since anything to the zero power is one.

Notice that  since anything times zero is zero.

Simplify.

As stated before, anything to the zero power is one.

Example Question #9 : Derivative Defined As The Limit Of The Difference Quotient

What is the derivative of ?

Explanation:

To find the first derivative, we can use the power rule. We lower the exponent on all the variables by one and multiply by the original variable.

Anything to the zero power is one.

Example Question #10 : Derivative Defined As The Limit Of The Difference Quotient

What is the derivative of ?

Explanation:

To find the first derivative, we can use the power rule. We lower the exponent on all the variables by one and multiply by the original variable.

We're going to treat  as  since anything to the zero power is one.

For this problem that would look like this:

Notice that  since anything times zero is zero.

Example Question #31 : Calculus I — Derivatives

What is the derivative of ?

Explanation:

To find the first derivative, we can use the power rule. To do that, we lower the exponent on the variables by one and multiply by the original exponent.

We're going to treat  as  since anything to the zero power is one.

Notice that  since anything times zero is zero.

Example Question #11 : Finding Derivatives

Explanation:

To find the derivative of the problem, we can use the power rule. The power rule says to multiply the coefficient of the variable by the exponent of the variable and then lower the exponent value by one.

To make that work, we're going to treat  as , since anything to the zero power is one.

This means that  is the same as .

Now use the power rule:

Anything times zero is zero.

Example Question #12 : Finding Derivatives

What is the first derivative of ?

Explanation:

To find the derivative of , we can use the power rule.

The power rule states that we multiply each variable by its current exponent and then lower the exponent of each variable by one.

Since , we're going to treat  as .

Anything times zero is zero, so our final term , regardless of the power of the exponent.

Simplify what we have.

Our final solution, then, is .