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

Using the reduction formulas for products of powers or sin and cosine

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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.

Given vectors $\boldsymbol{a,\;b}$, find $\boldsymbol{a\times b}$

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Find the dot product and the angle between two vectors

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

Differentiation of  polynomials, cos, sin, exp, log functions. Product, quotient and chain rules.

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Harder implicit differentiation requiring both chain rule and product rule.

Differentiation of  polynomials, cos, sin, exp, log functions. Product, quotient and chain rules.

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Intorduces students to the definition of a function $f:A\mapsto B$ as a subset of the Cartesian product $A\times B$.

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

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

Differentiation of  polynomials, cos, sin, exp, log functions. Product, quotient and chain rules.

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Find the dot product and the angle between two vectors

Given vectors $\boldsymbol{a,\;b}$, find $\boldsymbol{a\times b}$

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Use the product rule to differentiate various functions.

Integrate the product of two functions by the method of integration by parts.

The derivative of $\displaystyle x ^ {m}(ax^2+b)^{n}$ is of the form $\displaystyle x^{m-1}(ax^2+b)^{n-1}g(x)$. Find $g(x)$.

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

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

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

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 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 $f\;'(x)= (a + b x)^{m-1}  e ^ {n x}g(x)$.

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Differentiation of  polynomials, cos, sin, exp, log functions. Product, quotient and chain rules.

rebelmaths