6.1 and 6.2

6.1 and 6.2

\[\begin{array}\ &\text{Primary Formulas}\\ &{[C]′[et]′[sint]′=0=et=cost[tn]′[lnt]′[cost]′=ntn−1=1t=−sint(6.1)(6.1)[C]′=0[tn]′=ntn−1[et]′=et[ln⁡t]′=1t[sin⁡t]′=cos⁡t[cos⁡t]′=−sin⁡t\begin{array}\ {[C]^{\prime} } &=0 & {\left[t^{n}\right]^{\prime} } &=n t^{n-1} \\ {\left[e^{t}\right]^{\prime} } &=e^{t} & {[\ln t]^{\prime} } &=\frac{1}{t} \\ {[\sin t]^{\prime} } &=\cos t & {[\cos t]^{\prime} } &=-\sin t \\ \end{array}}\\ &\text{Combination Formulas}\\ &{[u+v]′[uv]′[G(u)]′=[u]′+[v]′=[u]′v+u[v]′=G′(u)u′[Cu]′[uv]′=C[u]′=v[u]′−u[v]′u2(6.2)(6.2)[u+v]′=[u]′+[v]′[Cu]′=C[u]′[uv]′=[u]′v+u[v]′[uv]′=v[u]′−u[v]′u2[G(u)]′=G′(u)u′\begin{array}\ {[u+v]^{\prime} } &=[u]^{\prime}+[v]^{\prime} & {[C u]^{\prime} } &=C[u]^{\prime} \\ {[u v]^{\prime} } &=[u]^{\prime} v+u[v]^{\prime} & {\left[\frac{u}{v}\right]^{\prime} } &=\frac{v[u]^{\prime}-u[v]^{\prime}}{u^{2}} \\ {[G(u)]^{\prime} } &=G^{\prime}(u) u^{\prime} & & \end{array}}\\ \end{array}\]

[ln(1−t

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C

Example 12.7.3, Equations 12.22 and 12.23.

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Chapter 17

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Figure 9.13

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F(x)=cosxF(x)=cos⁡xF(x) = \cos x and F(x)=cosx and

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0,5

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