Differentiate \(e^x\).

Differentiate \(\sin x\).

Differentiate \(\cos x\).

Differentiate \(\ln x\), stating the domain condition.

Differentiate \(x^7\).

Differentiate \(\tan x\).

Differentiate \(3e^x-2\sin x\).

Differentiate \(4\ln x+\cos x\).

Find \(f'(x)\) for \(f(x)=x^3+e^x-\cos x\).

Find the derivative of \(f(x)=\arctan x+\arcsin x\).

Differentiate \(f(x)=x^{-2}+\ln x\).

At \(x=0\), find the slope of \(y=\sin x+e^x\).

Differentiate \(f(x)=\sec^2x+\tan x\), using \(\frac{d}{dx}\tan x=\sec^2x\) and the power rule only where valid.

Find \(f'(1)\) for \(f(x)=x^4+2\ln x-e^x\).

Find \(a\) if \(f(x)=ax^3+\sin x\) has \(f'(0)=5\).

Find \(a\) so that \(f(x)=ae^x+x^2\) has \(f'(0)=7\).

Find all \(x>0\) where the derivative of \(f(x)=\ln x-x\) is zero.

A student writes \(\frac{d}{dx}\cos x=\sin x\). Diagnose the error.

Explain why \(\frac{d}{dx}\ln x=1/x\) should not be used at \(x=-2\) in a real-valued Level 1 setting.

Explain why memorising standard derivatives is not enough to differentiate every expression, using \(\sin(x^2)\) as an example.