Using the definition, calculate the derivatives of the function. Then

tricotasu 2021-09-28 Answered
Using the definition, calculate the derivatives of the function. Then find the values of the derivatives as specified.
g(t)=1t2;g(1),g(2),g(3)
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Expert Answer

casincal
Answered 2021-09-29 Author has 82 answers
Step 1
The given function is,
g(t)=1t2
To find the derivative of the function, we use the power rule of differentiation,
ddx(xn)=nxn1
Step 2
Applying differentiation on both sides of the function, we get
g(t)=ddt(1t2)
=ddt(t2)
=2t21
=2t3
=2t3
Therefore, the derivative of the given function is g(t)=2t3
Step 3
Finding the value of the derivative of the given function for the specified value of the variable, we get
g(1)=2(1)3
=21
=2
g(2)=2(2)3
=28
=14
g(3)=2(3)3
=233
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