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Question 1 of 4
Find the derivative
f(x)=√x3
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First, convert the surd into an exponent.
f(x) |
= |
√x3 |
|
|
= |
x32 |
Convert the surd into an exponent |
Next, identify the values of the function
f(x) |
= |
xn |
|
f(x) |
= |
x32 |
Substitute the values into the power rule
f'(x) |
= |
nxn−1 |
|
|
= |
23⋅x23−1 |
Substitute known values |
|
|
= |
32x12 |
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Question 2 of 4
Find the derivative
f(x)=4√x
Incorrect
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First, convert the surd into an exponent.
f(x) |
= |
4√x |
|
|
= |
x14 |
Convert the surd into an exponent |
Next, identify the values of the function
f(x) |
= |
xn |
|
f(x) |
= |
x14 |
Substitute the values into the power rule
f'(x) |
= |
nxn−1 |
|
|
= |
14⋅x14−1 |
Substitute known values |
|
|
= |
14x−34 |
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Question 3 of 4
Find the derivative
f(x)=4√x+x√x
Incorrect
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First, convert the surd into an exponent.
First term:
f(x) |
= |
4√x +x√x |
|
|
= |
4x12+x√x |
Convert the surd into an exponent |
Second term:
f(x) |
= |
4x12+ x√x |
|
|
= |
4x12+ x1×x12 |
Convert the surd into an exponent |
|
|
= |
4x12+x32 |
Next, identify the values of the function
First term:
f(x) |
= |
xn |
|
f(x) |
= |
4x12+x32 |
Second term:
f(x) |
= |
xn |
|
f(x) |
= |
4x12+x32 |
Substitute the values into the power rule
First term:
f'(x) |
= |
nxn−1 |
|
|
= |
12⋅4x12−1+x32 |
Substitute known values |
|
|
= |
2x−12 |
Second term:
f'(x) |
= |
nxn−1 |
|
|
= |
2x−12+32⋅x32−1 |
Substitute known values |
|
|
= |
2x−12+32x12 |
f'(x)=2x−12+32x12
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Question 4 of 4
Find the derivative
f(x)=1x2√x
Incorrect
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First, convert the surd into an exponent.
f(x) |
= |
1x2√x |
|
|
= |
1x2×x12 |
Convert the surd into an exponent |
|
|
= |
1x52 |
Next, reciprocate x52 to remove the exponent from the denominator
f(x) |
= |
1x52 |
|
|
= |
x−52 |
Reciprocate x52 |
Next, identify the values of the function
f(x) |
= |
xn |
|
f(x) |
= |
x−52 |
Substitute the values into the power rule
f'(x) |
= |
nxn−1 |
|
|
= |
−52⋅x−52−1 |
Substitute known values |
|
|
= |
−52x−72 |
f'(x)=−52x−72