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Question 1 of 5
Find the derivative
f(x)=1(5-4x5)2
Incorrect
First, remove the fraction by reciprocating the denominator
Next, identify the values of the function
f(x) |
= |
xn |
f(x) |
= |
(5−4x5)−2 |
Finally, substitute the values into the chain rule
y’ |
= |
n⋅(f(x))n−1⋅f′(x) |
|
= |
−2⋅(5−4x5)(−2)−1⋅f′(5−4x5) |
Substitute known values |
|
= |
−2(5−4x5)−3⋅(−20x4) |
Differentiate 5-4x5 |
|
= |
40x4(5−4x5)−3 |
Evaluate |
|
|
= |
40x4(5-4x5)3 |
Reciprocate (5-4x5)-3 |
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Question 2 of 5
Find the derivative
f(x)=√16-x2
Incorrect
First, convert the surd into an exponent.
Next, identify the values of the function
f(x) |
= |
xn |
|
f(x) |
= |
(16−x2)12 |
Finally, substitute the values into the chain rule
y’ |
= |
n⋅(f(x))n−1⋅f′(x) |
|
|
= |
12⋅(16−x2)12−1⋅f′(16−x2) |
Substitute known values |
|
|
= |
12(16−x2)−12⋅(−2x) |
Differentiate 16-x2 |
|
|
= |
−x(16−x2)−12 |
Evaluate |
|
|
= |
-x(16-x2)12 |
Reciprocate (16-x2)-12 |
|
|
= |
-x√16-x2 |
Convert the exponent into a surd |
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Question 3 of 5
Find the derivative
f(x)=(x4+4x)14
Incorrect
First, identify the values of the function
f(x) |
= |
xn |
|
f(x) |
= |
(x4+4x)14 |
Next, substitute the values into the chain rule
y’ |
= |
n⋅(f(x))n−1⋅f′(x) |
|
|
= |
14⋅(x4+4x)14−1⋅f′(x4+4x) |
Substitute known values |
|
|
= |
14(x4+4x)−34⋅(4x3+4) |
Differentiate x4+4x |
|
|
= |
x3+1(x4+4x)−34 |
Evaluate |
|
|
= |
x3+1(x4+4x)34 |
Reciprocate (x4+4x)-34 |
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Question 4 of 5
Find the derivative
f(x)=√5-6x
Incorrect
First, convert the surd into an exponent.
Next, identify the values of the function
f(x) |
= |
xn |
|
f(x) |
= |
(5−6x)12 |
Finally, substitute the values into the chain rule
y’ |
= |
n⋅(f(x))n−1⋅f′(x) |
|
|
= |
12⋅(5−6x)12−1⋅f′(5−6x) |
Substitute known values |
|
|
= |
12(5−6x)−12⋅(−6) |
Differentiate 5-6x |
|
|
= |
−3(5−6x)−12 |
Evaluate |
|
|
= |
-3(5-6x)12 |
Reciprocate (5-6x)-12 |
|
|
= |
-3√5-6x |
Convert the exponent into a surd |
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Question 5 of 5
Find the derivative
f(x)=2√1-2x
Incorrect
First, convert the surd into an exponent.
Next, remove the fraction by reciprocating the denominator
Next, identify the values of the function
f(x) |
= |
xn |
|
f(x) |
= |
2(1−2x)−12 |
Finally, substitute the values into the chain rule
y’ |
= |
n⋅(f(x))n−1⋅f′(x) |
|
|
= |
−12⋅2(1−2x)−12−1⋅f′(1−2x) |
Substitute known values |
|
|
= |
−1(1−2x)−32⋅(−2) |
Differentiate 1-2x |
|
|
= |
2(1−2x)−32 |
Evaluate |
|
|
= |
2(1-2x)32 |
Reciprocate (1-2x)-32 |
|
|
= |
2√(1-2x)3 |
Convert the exponent into a surd |