143 results authored by Marlon Arcila - search across all users.

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• Question

A basic introduction to differentiation

• Question in Limites

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• Question in Limites

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• Question

Implicit differentiation.

Given $x^2+y^2+dxy +ax+by=c$ find $\displaystyle \frac{dy}{dx}$ in terms of $x$ and $y$.

Also find two points on the curve where $x=0$ and find the equation of the tangent at those points.

• Question

Implicit differentiation.

Given $x^2+y^2+ax+by=c$ find $\displaystyle \frac{dy}{dx}$ in terms of $x$ and $y$.

• Question

Using differentiation to find the tangent and normal to a line at a given point

• Question

Real life problems with differentiation

• Question

$\displaystyle ax^b+\frac{c}{x^{d}}+f$ at $x=n$

• Question

Finding the stationary points of a cubic with two turning points

• Question

Differentiating the natural logarithm

• Question

$2e^{x^3}+4e^x$

• Question

$2e^{x^3}+4e^x$

• Question

$2e^{x^3}+4e^x$

• Question

Differentiate $f(x) = (a x + b)/ \sqrt{c x + d}$ and find $g(x)$ such that $f^{\prime}(x) = g(x)/ (2(c x + d)^{3/2})$.

• Question

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

• Question

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

• Question

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

• Question

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

• Question

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

• Question

Using the chain rule within product rule problems

• Question

More work on differentiation with trigonometric functions

• Question

More work on differentiation with trigonometric functions

• Question

Differentiation of trigonometric functions

• Question

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• Question

More work on differentiation with fractional coefficients

• Question

More work on differentiation with fractional coefficients and powers

• Question

More work on differentiation with fractional coefficients

• Question

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• Question

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• Question in JSXGraph

Given a graph of a line of the form $y=ax+b$ where $a$ and $b$ are integers, find the equation of the line. The y-intercept is given.