John Rhodes, Math Teacher at Senioritis.io

John Rhodes
June 21, 2023
Calculus

Learn How To Use The Chain Rule For Finding Derivatives With This Step-By-Step Guide

Let f be a differentiable function. If h(x)=(1+f(3x))2, which of the following gives a correct process for finding h′(x) ? Correct. This requires using the chain rule...

John Rhodes
June 21, 2023
Calculus

How To Find The Slope Of A Line Tangent To A Curve Using Implicit Differentiation: A Step-By-Step Guide

What is the slope of the line tangent to the curve y3−xy2+x3=5 at the point (1,2) ? Correct. The point (1,2)(1,2) is on the curve since x=1x=1,...

John Rhodes
June 21, 2023
Calculus

Learn How To Find Dy/Dx With Ease – Step By Step Guide

If sin(x+y)=3x−2y, then dydx= Correct. The chain rule is the basis for implicit differentiation as well as the differentiation of a composite function. cos(x+y)(1+dydx)=3−2dydxcos(x+y)(1+dydx)=3−2dydx cos(x+y)+cos(x+y)dydx=3−2dydxcos(x+y)+cos(x+y)dydx=3−2dydx (2+cos(x+y))dydx=3−cos(x+y)(2+cos(x+y))dydx=3−cos(x+y) dydx=3−cos(x+y)2+cos(x+y)...

John Rhodes
June 21, 2023
Calculus

How To Find Derivatives Using Implicit Differentiation: Example With F(X)G(Y) = 17 – X – Y

The point (−2,4) lies on the curve in the xy-plane given by the equation f(x)g(y)=17−x−y, where f is a differentiable function of x and g is a...

John Rhodes
June 21, 2023
Calculus

Finding F(0) And G'(2) Using Inverse Function Theorem In Math – Step By Step Guide

Let f be the increasing function defined by f(x)=x3+2×2+4x+5, where f(−1)=2. If g is the inverse function of f, which of the following is a correct expression...

John Rhodes
June 21, 2023
Calculus

How To Find The Derivative Of An Inverse Function: Step-By-Step Guide With Examples.

The table above gives selected values for a differentiable and decreasing function f and its derivative. If g(x)=f−1(x) for all x, which of the following is a...

John Rhodes
June 21, 2023
Calculus

How To Differentiate Sin⁻¹(X) Using The Chain Rule | Math Tutorial And Example Problem

ddx(sin−1x)∣∣x=12= Correct. If y=sin−1xy=sin⁡−1x, then siny=xsin⁡y=x. Using the chain rule to differentiate this implicit relation gives cosydydx=1⇒dydx=1cosycos⁡ydydx=1⇒dydx=1cos⁡y. Since y=sin−1xy=sin⁡−1x implies that −π2≤y≤π2−π2≤y≤π2, the value of cosycos⁡y is...

John Rhodes
June 21, 2023
Geometry

Mastering Trapezoids: Bases, Lengths, And Area Calculation.

Bases of a trapezoid The parallel sides a trapezoid. A trapezoid is a quadrilateral with one pair of parallel sides and the other pair of non-parallel sides....