Content created by Newcastle University

Differentiate the function $f(x)=(a + b x)^m  e ^ {n x}$ using the product rule. Find $g(x)$ such that $f\;'(x)= (a + b x)^{m-1}  e ^ {n x}g(x)$.

Differentiate the function $(a + b x)^m  e ^ {n x}$ using the product rule.

Differentiate $f(x)=x^{m}\sin(ax+b) e^{nx}$.

The answer is of the form:
$\displaystyle \frac{df}{dx}= x^{m-1}e^{nx}g(x)$ for a function $g(x)$.

Find $g(x)$.

Differentiate $ (a+bx) ^ {m} \sin(nx)$

Differentiate the following functions: $\displaystyle x ^ n \sinh(ax + b),\;\tanh(cx+d),\;\ln(\cosh(px+q))$

Differentiate the following functions: $\displaystyle x ^ n \sinh(ax + b),\;\tanh(cx+d),\;\ln(\cosh(px+q))$

Differentiate $f(x) = x^m(a x+b)^n$.

Differentiate $x^m\cos(ax+b)$

Differentiate $ \sin(ax+b) e ^ {nx}$.

Differentiate $\displaystyle \frac{ax+b}{cx+d}$.

The derivative of $\displaystyle \frac{ax+b}{cx^2+d}$ is of the form $\displaystyle \frac{g(x)}{(cx^2+d)^2}$. Find $g(x)$.

No description given

No description given

No description given

No description given

No description given

Use the quotient rule to differentiate various functions.

Calculate the Pearson correlation coefficient on paired data and comment on the significance.

Calculate the Pearson correlation coefficient on paired data and comment on the significance.

Spearman rank correlation calculated. 10 paired observations.

Spearman rank correlation calculated. 8 paired observations.

Cauchy's integral theorem/formula for several functions $f(z)$ and $C$ the unit circle.

Differentiate $\displaystyle e^{ax^{m} +bx^2+c}$

Differentiate the following functions: $\displaystyle x ^ n \sinh(ax + b),\;\tanh(cx+d),\;\ln(\cosh(px+q))$

Write complex numbers in real-imaginary form.

Poles, residues, and contour integral of a complex-valued function.  Pair of pure imaginary poles.

Poles, residues, and contour integral of a complex-valued function.  Pair of real poles.

Poles, residues, and contour integral of a complex-valued function.  Single, simple pole.