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Question 1 of 4
Find the derivative
f(x)=6x√x
Incorrect
First, convert the surd into an exponent.
f(x) |
= |
6x√x |
|
|
= |
6x1×x12 |
Convert the surd into an exponent |
|
|
= |
6x32 |
Next, reciprocate x32 to remove the exponent from the denominator
f(x) |
= |
6x32 |
|
|
= |
6x-32 |
Reciprocate x32 |
Next, identify the values of the function
Substitute the values into the power rule
f′(x) |
= |
nxn−1 |
|
|
= |
−32⋅6x−32−1 |
Substitute known values |
|
|
= |
-9x-52 |
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Question 2 of 4
Find the derivative
f(x)=√xx2
Incorrect
First, convert the surd into an exponent.
f(x) |
= |
√xx2 |
|
|
= |
x12x2 |
Convert the surd into an exponent |
Next, reciprocate x2 to remove the exponent from the denominator
f(x) |
= |
x12x2 |
|
|
= |
x12×x-2 |
Reciprocate x2 |
|
|
= |
x-32 |
Next, identify the values of the function
Substitute the values into the power rule
f′(x) |
= |
nxn−1 |
|
|
= |
−32⋅x−32−1 |
Substitute known values |
|
|
= |
-32x-52 |
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Question 3 of 4
Find the derivative
f(x)=x5(x-7)
Incorrect
First, distribute x5 to the value inside the parenthesis.
f(x) |
= |
x5(x-7) |
|
= |
(x×x5)-(7×x5) |
Distribute |
|
= |
x6-7x5 |
Next, identify the values of the function
Substitute the values into the power rule
First term:
f′(x) |
= |
nxn−1 |
|
= |
6⋅x6−1−7x5 |
Substitute known values |
|
= |
6x5-7x5 |
Second term:
f′(x) |
= |
nxn−1 |
|
= |
6x5−5⋅7x5−1 |
Substitute known values |
|
= |
6x5-35x4 |
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Question 4 of 4
Find the derivative
f(x)=(x+3)(2x+2)
Incorrect
Remember
Differentiating a constant makes it 0.
First, expand the equation.
f(x) |
= |
(x+3)(2x+2) |
|
= |
2x2+2x+6x+6 |
Expand |
|
= |
2x2+8x+6 |
Combine like terms |
Next, identify the values of the function
First term:
f(x) |
= |
xn |
f(x) |
= |
2x2+8x+6 |
Second term:
f(x) |
= |
xn |
f(x) |
= |
2x2+8x+6 |
Third term:
f(x) |
= |
xn |
f(x) |
= |
2x2+8x+6 |
Substitute the values into the power rule
First term:
f′(x) |
= |
nxn−1 |
|
= |
2⋅2x2−1+8x+6 |
Substitute known values |
|
= |
4x+8x+6 |
Second term:
f′(x) |
= |
nxn−1 |
|
= |
4x+1⋅81−1+6 |
Substitute known values |
|
= |
4x+8+6 |
Third term:
f′(x) |
= |
nxn−1 |
|
= |
4x+8+0 |
Differentiating a constant makes it 0 |
|
= |
4x+8 |