AP Calculus AB 2.7 Derivatives of cos x, sin x, ex, and ln x - MCQs - Exam Style Questions
No-Calc Question
\(\ \displaystyle \frac{d}{dx}\left(x^{5}-5^{x}\right)=\)
(A) \(\dfrac{x^{6}}{6}-\dfrac{5^{x}}{\ln 5}\)
(B) \(5x^{4}-5^{x}\)
(C) \(5x^{4}-x\cdot 5^{x-1}\)
(D) \(5x^{4}-(\ln 5)\,5^{x}\)
(B) \(5x^{4}-5^{x}\)
(C) \(5x^{4}-x\cdot 5^{x-1}\)
(D) \(5x^{4}-(\ln 5)\,5^{x}\)
▶️ Answer/Explanation
\(\dfrac{d}{dx}(x^{5})=5x^{4}\).
\(\dfrac{d}{dx}(5^{x})=(\ln 5)\,5^{x}\).
Combine with minus sign: \(5x^{4}-(\ln 5)\,5^{x}\).
✅ Answer: (D)