From f4505a6d72d34d732351f0802c7262366a9fbe4c Mon Sep 17 00:00:00 2001 From: arc Date: Sun, 13 Apr 2025 17:26:02 -0600 Subject: [PATCH] vault backup: 2025-04-13 17:26:02 --- education/math/MATH1210 (calc 1)/Derivatives.md | 6 +++--- 1 file changed, 3 insertions(+), 3 deletions(-) diff --git a/education/math/MATH1210 (calc 1)/Derivatives.md b/education/math/MATH1210 (calc 1)/Derivatives.md index ac075e4..1ef3a4e 100644 --- a/education/math/MATH1210 (calc 1)/Derivatives.md +++ b/education/math/MATH1210 (calc 1)/Derivatives.md @@ -158,9 +158,9 @@ This is used when you want to take the derivative of a function raised to a func > Find the derivative of the function $y = (2x \sin x)^{3x}$ 5. $\ln y = \ln (3x \sin x)^{3x}$ -6. $\ln y = 3x * \ln(2x \sin x)$* +6. $\ln y = 3x * \ln(2x \sin x)$ 7. $\dfrac{d}{dx} \ln(y) = \dfrac{d}{dx} 3x(\ln 2 + \ln x + \ln(sinx))$ -8. $\dfrac{1}{y} \dfrac{dy}{dx} = 3(\ln 2 + \ln x + \ln(\sin(x))) + 3x (0 + \dfrac{1}{x} + \dfrac{1}{\sin x} * \cos x)$j +8. $\dfrac{1}{y} \dfrac{dy}{dx} = 3(\ln 2 + \ln x + \ln(\sin(x))) + 3x (0 + \dfrac{1}{x} + \dfrac{1}{\sin x} * \cos x)$ 9. $\dfrac{dy}{dx} = (3\ln 2 + 3 \ln x + 3\ln \sin(x) + 3\ln(\sin(x) + 3x\cot(x))(2x\sin x)^{3x}$ # Chain Rule $$ \dfrac{d}{dx} f(g(x)) = f'(g(x))*g'(x) $$ @@ -209,5 +209,5 @@ $$ \dfrac{d}{dx}(\arcsin(x) = \dfrac{1}{\sqrt{1-x^2}}$$ Given these facts: 12. Let $y$ be some function of $x$ 13. $\dfrac{d}{dx} x = 1$ -14. $\dfrac{d}{dx} y = \dfrac{dy}{dx}$\ +14. $\dfrac{d}{dx} y = \dfrac{dy}{dx}$