State the chain rule for \(y=f(u)\) and \(u=g(x)\).

For \(y=(3x+1)^5\), identify a suitable inner function \(u\).

Differentiate \(y=(2x-7)^4\).

Differentiate \(y=\sin(5x)\).

Differentiate \(f(x)=\sqrt{4x+9}\).

Differentiate \(y=\cos(x^2)\).

Differentiate \(y=(x^2+3x)^6\).

Differentiate \(y=e^{2x^2-1}\).

Differentiate \(y=\ln(1+3x^2)\).

Find \(d(\tan(4x-1))/dx\).

Differentiate \(y=\sin^3(2x)\), where \(\sin^3(2x)=(\sin(2x))^3\).

A position is \(s(t)=(t^2+1)^4\). Find the velocity \(v(t)\).

Differentiate \(y=\sqrt{\sin x}\), stating where the derivative formula is defined.

Differentiate \(y=\ln(\cos x)\), and state the needed domain condition.

Differentiate \(y=(1+x^2)^{-3}\) and simplify without negative exponents.

For \(y=(a x+b)^n\), where \(a,b,n\) are constants, find \(dy/dx\).

Differentiate \(y=\sin((3x+1)^2)\).

A student writes \(d(\sin(x^2))/dx=\cos x^2\). Explain the error and give the correct derivative.

Find all \(x\) where the tangent to \(y=(x^2-4)^3\) is horizontal.

Show why the derivative of \(f(g(x))\) is not usually \(f'(x)g'(x)\). Use \(f(u)=u^2\), \(g(x)=3x+1\).