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Tag: derivative

calculus

Calculus: the derivative: the power rule

Jack Jul 19, 2026 Tagged with constant multiple rule, constant rule, derivative, power rule, sum rule

Tutoring first-year calculus, finding derivatives is prominent. The tutor gives an example. The following is by my understanding. In yesterday’s post I mention finding relative extrema by solving for when the derivative is equal to zero. To begin with, how …

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calculus

Calculus: things calculus can do: local extrema

Jack Jul 18, 2026 Tagged with derivative, polynomial, quadratic, relative extrema

Tutoring calculus, you might hear curiosity about what it’s used for. The tutor mentions local extrema. In high school algebra, one can learn to expect that the graph y=2x^3 +10x^2 -11x -14 might have one relative minimum and one relative …

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calculus

Calculus: what is the derivative?

Jack Jul 17, 2026 Tagged with derivative

Tutoring calculus, derivatives are often visited. Yet, what is the derivative? In calculus, the derivative means the slope of a line tangent to the curve at that point. In other words, it means the direction the graph would follow from …

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calculus

Calculus: why the derivative of tanx is (secx)^2

Jack May 6, 2024 Tagged with derivative, quotient rule, trig derivatives, verifying differentiation formula

Tutoring calculus, everyday formulas students count on can often be verified. The tutor mentions the derivative of tanx. It’s true that (tanx)’ = (secx)^2. But why? Realizing tanx = sinx/cosx, then using the the quotient rule (u/v)’ = (vu’ – …

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Calculator Usage, calculus, math

Calculator usage: finding the derivative with the Sharp EL-520W

Jack Oct 26, 2015 Tagged with derivative, sharp el-520W

The tutor shares how to find the derivative with the Sharp EL-520W. To my knowledge, the Sharp EL-520W won’t give the symbolic derivative. Rather (as you’d likely expect anyway), it evaluates a function’s derivative at the x value the user …

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