Using the definition, calculate the derivatives of the function. Then find the values of the derivatives as specified. g(t)=\frac{1}{t^{2}}. g'(-1), g'(2), g'(\sqrt{3})

nitraiddQ

nitraiddQ

Answered question

2021-05-26

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)

Answer & Explanation

Macsen Nixon

Macsen Nixon

Skilled2021-05-27Added 117 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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