For example, if y = xx , then log y = x log x1/y. dy/dx = log x + 1dy/dx = y. (logx + 1)= xx (logx + 1)Higher-Order DifferentiationWe find higher-order derivatives on successive differentiation. The further differentiation of the first derivative is denoted by f'' or d2...
第3章 微分(Differentiation) 目錄 3.1切線...29 3.2導函數...30 3.3微分公式...32 3.4連鎖律...33 3.5高階導函數...33 3.6隱函數微分...34 3.7三角函數的導函數...
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Use logarithmic differentiation to find the derivative of y : y = x^{7sinx}. Use logarithmic differentiation to find the derivative of y=\sqrt{\frac{(3x-4)^5}{(x^2+2)^3. Use logarithmic differentiation to find the derivative of y = (sin(x))...
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Implicit differentiation is an important concept of mathematics that is applied to evaluate the derivative in those cases in which the equation is of the form h(x,y)=constant. Rules of differentiation that we require in this problem are: ddx(u⋅v)=uv′+vu′ddx(c...
Example 2:Find the derivative of the implicit function x + Sinxy - y = 0 Solution: The given function is x + Sinxy - y = 0 Here we differentiate the function with respect to x. d/dx.x + d/dx.Sinxy - d/dx.y = 0 1 + Cosxy.(d/dx.xy) - dy/dx = 0 ...
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Dcosx =−sinx (derivatives of cotrigs always have minus signs.) Dtanx =sec 2 x =1+tan 2 x Dsecx =secxtanx De x =e x Dlnx =1/x Domain of derivative: x >0. Dln|x| =1/x Darctanx =1/(1+x 2 ) Darcsinx =1/ √ 1−x 2 Darccosx =−1/ √ 1−x 2 2 Dcoshx...
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