143 results authored by Marlon Arcila - search across all users.
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A basic introduction to differentiation
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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.
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Implicit differentiation.
Given $x^2+y^2+ax+by=c$ find $\displaystyle \frac{dy}{dx}$ in terms of $x$ and $y$.
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Using differentiation to find the tangent and normal to a line at a given point
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Real life problems with differentiation
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$ \displaystyle ax^b+\frac{c}{x^{d}}+f$ at $x=n$
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Finding the stationary points of a cubic with two turning points
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Differentiating the natural logarithm
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$2e^{x^3}+4e^x$
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$2e^{x^3}+4e^x$
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$2e^{x^3}+4e^x$
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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})$.
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The derivative of $\displaystyle \frac{ax+b}{cx^2+d}$ is of the form $\displaystyle \frac{g(x)}{(cx^2+d)^2}$. Find $g(x)$.
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Differentiate $f(x) = x^m(a x+b)^n$.
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Differentiate the function $f(x)=(a + b x)^m e ^ {n x}$ using the product rule. Find $g(x)$ such that $f^{\prime}(x)= (a + b x)^{m-1} e ^ {n x}g(x)$.
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Differentiate $x^m\cos(ax+b)$
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Differentiate $ \sin(ax+b) e ^ {nx}$.
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Using the chain rule within product rule problems
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More work on differentiation with trigonometric functions
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More work on differentiation with trigonometric functions
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Differentiation of trigonometric functions
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More work on differentiation with fractional coefficients
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More work on differentiation with fractional coefficients and powers
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More work on differentiation with fractional coefficients
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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.
