High School Math : General Derivatives and Rules
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Example Questions
Example Question #1 : Derivative Defined As The Limit Of The Difference Quotient
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 
 "\frac{\mathrm{d} }{\mathrm{d} x}(6x^2+8)=(2*6x^{2-1})+(0*8x^{0-1})")
Notice that 
Example Question #2 : Derivative Defined As The Limit Of The Difference Quotient
What is the derivative of 
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 
Notice that 
That leaves us with 
Simplify.
As stated earlier, anything to the zero power is one, leaving us with:
Example Question #3 : Derivative Defined As The Limit Of The Difference Quotient
What is the derivative of 
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 
 "\frac{\mathrm{d} }{\mathrm{d} x}(12x^2+13x+4)=(2*12x^{2-1})+(1*13x^{1-1})+(0*4x^{0-1})")
Notice that 
Just like it was mentioned earlier, anything to the zero power is one.
Example Question #4 : Derivative Defined As The Limit Of The Difference Quotient
What is the derivative of 
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 #5 : Derivative Defined As The Limit Of The Difference Quotient
What is the derivative of 
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 
Notice that 
Simplify.
As stated before, anything to the zero power is one.
Example Question #6 : Derivative Defined As The Limit Of The Difference Quotient
What is the derivative of 
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 #7 : Derivative Defined As The Limit Of The Difference Quotient
What is the derivative of 
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 
For this problem that would look like this:
Notice that 
Example Question #1171 : Ap Calculus Ab
What is the derivative of 
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 
 "\frac{\mathrm{d} }{\mathrm{d} x}(x^3+2x^2+5)=(3*x^{3-1})+(2*2x^{2-1})+(0*5x^{0-1})")
Notice that 
Example Question #15 : Finding Derivatives
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 
This means that 
Now use the power rule:
Anything times zero is zero.
Example Question #16 : Finding Derivatives
What is the first derivative of 
To find the derivative of 
The power rule states that we multiply each variable by its current exponent and then lower the exponent of each variable by one.
Since 
Anything times zero is zero, so our final term 
Simplify what we have.
Our final solution, then, is 
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