Calculating the derivative of a function of the form $\frac{ax^n+bx^m}{cx^p+d}$ using the quotient rule.

Calculating the derivative of a function of the form $\frac{ax^n}{bx+c}$ using the quotient rule.

Calculating the derivative of a function of the form $(ax+b)^n(cx+d)^m$ using the product rule.

Calculating the derivative of a function of the form $ax^n(bx^m+c)^p$ using the product rule.

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

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

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

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

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

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

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

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

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

Calculating the derivative a function of the form $ax^n \tan(bx)$ using the product rule.

Calculating the derivative a function of the form $ax^n \cos(bx)$ using the product rule.

Calculating the derivative a function of the form $ax^n \sin(bx)$ using the product rule.

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 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.