"Find the first and second derivatives y=6x2−10x−5x−2" was answered by our community

Joseph Krupa

Answered question

2021-12-10

Find the first and second derivatives

y = 6 x^{2} - 10 x - 5 x^{- 2}

chumants6g

Beginner2021-12-11Added 33 answers

Step 1
We have given a function;

y = 6 x^{2} - 10 x - 5 x^{- 2}

Step 2
To find the derivative we use the formula;

\frac{d}{d x} (x^{n}) = n x^{n - 1}

The first derivative of the function will be;

\frac{d y}{d x} = 12 x - 10 + 10 x^{- 3}

f^{'} = 12 x - 10 + 10 x^{- 3}

When we differentiate again we get the second derivative of the function.

f^{‴} = 12 - 30 x^{- 4}

Since the derivative of constant is always zero, so d/dx(10)=0
Step 3
Hence, the first derivative of the function is

f^{'} = 12 x - 10 + 10 x^{- 3}

and the second derivative is

f^{″} = 12 - 30 x^{- 4}

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