객관식
Find the indicated derivative.
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3. Techniques of Differentiation
Basic Rules of Differentiation
객관식
Find the indicated derivative.
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검증된 단계별 안내1
Identify the function to differentiate: The given function is \(-5t\), where \(t\) is the variable.
Recall the power rule for differentiation: \(\frac{d}{dt}[t^n] = n \cdot t^{n-1}\). For a constant multiplied by a variable, the constant remains, and the power rule is applied to the variable.
Apply the power rule to \(-5t\): Rewrite \(-5t\) as \(-5 \cdot t^1\). Differentiating this gives \(-5 \cdot 1 \cdot t^{1-1}\).
Simplify the expression: \(-5 \cdot 1 \cdot t^{1-1}\) simplifies to \(-5 \cdot t^0\). Since \(t^0 = 1\), the result becomes \(-5\).
Conclude that the derivative of \(-5t\) with respect to \(t\) is \(-5\).
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