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Introduction to Differential Equations. Separable Equations. Exponential Growth and Decay. Free Calculus worksheets created with Infinite Calculus. Printable in convenient PDF format.
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Worksheet on Logarithmic Differentiation (Solutions) Math 1a: Introduction to Calculus 21 March 2005 For each of the following, differentiate the function first using any rule you want, then using logarithmic differentiation: 1. y = x2 Solution. If y = x2, then lny = ln(x2) = 2lnx. Differentiating, 1 y dy dx = 2 x, so dy dx = 2y x = 2x2 x ...
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Differentiation - Natural Logs and Exponentials. Differentiate each function with respect to x. 1) y = ln x3. 3) y = ln ln 2 x4. 5) y = cos ln 4 x3. ( 4 x3 + 5)2. 7) y = e. 4 x4. 9) y = ln ( − x3 − 3 )5.
Worksheet by Kuta Software LLC. Kuta Software - Infinite Calculus. Differentiation - Logs and Exponentials. Differentiate each function with respect to x. 1) y = 44 x4. dy. = 44 x4. ln 4 ⋅ 16 x3 dx. 4 x4 + 2 = x3 ⋅ 4 ln 4. 3) y = log 3 x2. dy 1. = ⋅ 6 x dx 3 x2 ln 3. 2. = xln 3.
Worksheet on Logarithmic Differentiation Math 1a: Introduction to Calculus 21 March 2005 For each of the following, differentiate the function first using any rule you want, then using logarithmic differentiation: 1. y = x2 2. y = ex 3. y = √ x2 +1 4. y = xsinx 5. y = x x2+2 6. y = p (x2 +1)(x−1)2.
The first is for polynomials. When taking the derivative of a polynomial, we use the power rule (both basic and with chain rule): d dx xn= nxn - 1. d dx (f(x))n= n((f(x))n - 1\cdot f\prime (x). This rule is used when we run into a function of xbeing raised to a power than is a constant.
