Calculus
- \( \frac{d}{dx}\left(\frac{1}{x^2}\right) \)
- \( \frac{d}{dx}\left(x^{\frac{1}{2}}\right) \)
- \(\dfrac{d}{dx}\left(n^{x}\right)\)
- \(\displaystyle \frac{d}{dx}\left(2e^{x}\right)\)
- \(\displaystyle \frac{d}{dx}\ln\left(x^2\right)\)
- \(\frac{d}{dx}\left(5^x\right)\)
- \(\frac{d}{dx}\left(5e^x\right)\)
- \(\frac{d}{dx}\left(xe^x\right)\)
- \(\frac{d}{dx}\sec^2(x)\)
- \[ \frac{d}{dx} \left( 7^{x} \right) \]
- \[ \frac{d}{dx}(x+y) \]
- \[ \frac{d}{dx}\left(\frac{6}{x}\right) \]
- \[ \frac{d}{dx}\left(\sin^2(x)\right) \]
- \[ \frac{d}{dx}\left(\sin\left(x^2\right)\right) \]
- \[ \frac{d}{dx}\left(10^x\right) \]
- \[ \frac{d}{dx}\left(3^x\right) \]
- \[ \frac{d}{dx}\left(3e^x\right) \]
- \[ \frac{d}{dx}\left(4^x\right) \]
- \[ \frac{d}{dx}\left(4e^{x}\right) \]
- \[ \frac{d}{dx}\left(b^{x}\right) \]
- \[ \frac{d}{dx}\left(e^{-x}\right) \]
- \[ \frac{d}{dx}\left(e^{x^2}\right) \]
- \[ \frac{d}{dx}\left(x^{2}\right) \]
- \[ \frac{d}{dx}\left(x^{3}\right) \]
- \[ \frac{d}{dx}\left(x^{4}\right) \]
- \[ \frac{d}{dx}\left(x^x\right) \]
- \[ \frac{dy}{dx}=\frac{x}{y}. \]
- \[ \text{Find the derivative of } \cos^{2}(x). \]
- \[ \text{Find the derivative of } 2^x. \]
- \[\frac{d}{dx}\left(\frac{1}{\sqrt{x}}\right)\]
- \[\frac{d}{dx}\left(x^{e}\right)\]
- Find the derivative of \(e^{\frac{1}{x}}\).
- Is \(f(x)=e\) convergent or divergent?
- Maximum of \(13 \sqrt{x^2 – x^4} + 9 \sqrt{x^2 + x^4}\).
- Minimum of \(8^{x} + 8^{-x} – 4\left(4^{x} + 4^{-x}\right)\).
- Minimum value of \( (x+1)(x+2)(x+3)(x+4) \).
- The initial value problem is \(x'(t) = (t-1) x^2(t)\), \(x(0) = -8\). Find \(x(1)\).
- What is the derivative of \(e^x\)?
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