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

Differentiate $ (ax+b)^m(cx+d)^n$ using the product rule. The answer will be of the form $(ax+b)^{m-1}(cx+d)^{n-1}g(x)$ for a polynomial $g(x)$. Find $g(x)$.

Differentiate $ x ^ m(ax+b)^n$ using the product rule. The answer will be of the form $x^{m-1}(ax+b)^{n-1}g(x)$ for a polynomial $g(x)$. Find $g(x)$.

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

Differentiate $ x ^m \sqrt{a x+b}$.
The answer is in the form $\displaystyle \frac{x^{m-1}g(x)}{2\sqrt{ax+b}}$
for a polynomial $g(x)$. Find $g(x)$.

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

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

Calculations of the lengths of two 3D vectors, the distance between their terminal points, their sum, difference, and dot and cross products.

Product of one of 2, 3, 5, 9, or 10 by a number up to 10. With hints to learn calculation rather than memorisation.

Introduction to using the product rule

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

A mathematical expression part whose answer is the product of two matrices, $X \times Y$.

By setting the "variable value generator" option for $X$ and $Y$ to produce random matrices, we can ensure that the order of the factors in the student's answer matters: $X \times Y \neq Y \times X$.

Determine if various combinations of vectors are defined or not.

Given vectors $\boldsymbol{v}$ and $\boldsymbol{w}$, find their inner product.

Calculations of the lengths of two 3D vectors, the distance between their terminal points, their sum, difference, and dot and cross products.

Three 3 dim vectors, one with a parameter $\lambda$ in the third coordinate. Find value of $\lambda$ ensuring vectors coplanar. Scalar triple product.

Given vectors $\boldsymbol{A,\;B}$, find $\boldsymbol{A\times B}$

Questions on vector arithmetic and vector operations, including dot and cross product, as well as the vector equations of planes and lines.

Determine if various combinations of vectors are defined or not.

Find the cosine of the angle between two pairs of 3D and 4D vectors.

The calculations and answers are correct, however the Advice should display the interim calculations of the lengths of vectors and their products to say 6dps. At present the student may be mislead into using 2dps at each stage - the instruction at the start of Advice is somewhat confusing.

Find a unit vector orthogonal to two others.

Uses $\wedge$ for the cross product. The interim calculations should all be displayed to enough dps, not 3,  to ensure accuracy to 3 dps. If the cross product has a negative x component then it is not explained that the negative of the cross product is taken for the unit vector.

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Some more questions on set theory - covering set builder notation, cartesian products, complements.