MASH Bath: Question Bank

Calculating the derivative of a function of the form $\frac{(x-a)^2}{bx}$, finding its stationary points and determining their nature.

Finding the stationary points of a cubic equation and determining their nature.

Finding the stationary point of a function of the form $\frac{a \ln(x)}{x}$ and determining its nature.

Calculating $\frac{dy}{dx}$ from an implicit polynomial function.

Calculating $\frac{dy}{dx}$ from an implicit polynomial function.

Calculating $\frac{dy}{dx}$ from an implicit function.

Calculating $\frac{dy}{dx}$ from an implicit polynomial function.

Calculating the derivative of a function of the form $f(x)=\frac{x}{x+a}$ from first principles.

Calculating the derivative of a function of the form $f(x)=\frac{1}{ax}$ from first principles.

Calculating the derivative of a function of the form $f(x)=ax^2+bx+c$ from first principles.

Calculating the derivative of a function of the form $f(x)=ax^3$ from first principles.

Calculating the derivative of a function of the form $f(x)=ax+b$ from first principles.

Calculating the derivative of a function of the form $\sin(e^{ax})+b e^{\cos(cx)}$ using the chain rule.

Calculating the derivative of a function of the form $\ln(ax^n+\tan(bx+c))$ using the chain rule.

Calculating the derivative of a function of the form $\ln(ax^n+\cos(bx+c))$ using the chain rule.

Calculating the derivative of a function of the form $\ln(ax^n+\sin(bx+c))$ using the chain rule.

Calculating the derivative of a function of the form $\ln(ax^n+e^{bx})$ using the chain rule.

Calculating the derivative of a function of the form $\ln(ax^n+bx^m)$ using the chain rule.

Calculating the derivative of a function of the form $e^{\sin(ax+b)+\cos(cx+d)}$ using the chain rule.

Calculating the derivative of a function of the form $e^{\cos(ax+b)}$ using the chain rule.

Calculating the derivative of a function of the form $e^{\sin(ax+b)}$ using the chain rule.

Calculating the derivative of a function of the form $e^{ax^n+\ln(bx)+c}$ using the chain rule.

Calculating the derivative of a function of the form $e^{ax^n+bx^m}$ using the chain rule.

Calculating the derivative of a function of the form $e^{ax^2+bx+c}$ using the chain rule.

Calculating the derivative of a function of the form $\tan(a \ln(bx))$ using the chain rule.

Calculating the derivative of a function of the form $\cos(a \ln(bx))$ using the chain rule.

Calculating the derivative of a function of the form $\sin(a \ln(bx))$ using the chain rule.

Calculating the derivative of a function of the form $\tan(e^{ax}+bx^n)$ using the chain rule.

Calculating the derivative of a function of the form $\cos(e^{ax}+bx^n)$ using the chain rule.

Calculating the derivative of a function of the form $\sin(e^{ax}+bx^n)$ using the chain rule.