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Chapter 7: Problem 12

Find the derivative of the function. $$ y=t^{2}-6 $$

Short Answer

Expert verified
The derivative of the function \(y = t^{2} - 6\) is \(2t\).

Step by step solution

01

Identify the function and its components

In the function \(y = t^{2} - 6\), the term \(t^{2}\) is a power function and \(-6\) is a constant.
02

Applying the power rule

By applying the power rule, which states the derivative of \(t^n\) is \(n*\t^{n-1}\), to the term \(t^{2}\), the derivative is \(2t^{(2-1)} = 2t\).
03

Differentiating the constant

The derivative of a constant is always zero. Hence, the derivative of \(-6\) is zero.
04

Compile the total derivative

Combine the derivatives from Step 2 and Step 3 to find the total derivative of the function \(y = t^{2} - 6\). The derivative of the function is \(2t - 0 = 2t\).

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Most popular questions from this chapter

Identify the inside function, \(u=g(x)\), and the outside function, \(y=f(u)\). $$ y=f(g(x)) \quad u=g(x) \quad y=f(u) $$ $$ y=(x+2)^{-1 / 2} $$

Identify the inside function, \(u=g(x)\), and the outside function, \(y=f(u)\). $$ y=f(g(x)) \quad u=g(x) \quad y=f(u) $$ $$ y=(6 x-5)^{4} $$

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