Elements of the Differential Calculus
Elements of the Differential Calculus
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differential coefficients of u mth respect to X ; or separately considering the numerators and denominators, du, d^u, d^u, &c. denote the first, second, third, &c. dif- ferentials of -M supposing dx to be constant, and dx, dx^, dx^, &c. as before, indicate c&r, {dx)^^ (dxy, &c. or powers of dx.
Example 1. Let m = a?" ; then — = nar"""*, dx ^ = n(n-l)ar«-2, ^ = «(n-l)(n-2)a?«-3,&c., ^ = «(n--l)(n^2)(n-3) 1 = 1.2.3 ... .«.
JEx. 2. Let tt = e* ; then by (26), du . d'^u . d^u dx * dx'^^ * dx^ ' Ex.... 3. Let u = cos X ; then — = — sin a? = cos ( a? + - j» d'^u / . 27r\ -pj ac — cos X = COS I J? -f — j» ^ = smj? = cosf 4? + — j, &C , d^u ( , nir\ J^d?. 4. Let M = e* cos a? ; then --- = e* cos J? — e' sirf 0! = c* (cos ^r — sin x) dx =:>/2c*C0s(j? + ^j £l=vj..{o»(.+;)-™(.+|)} = (V2)2e'cosU + -^j &c. &c.
j5 = (V-.)".-(. + --f> Digitized by VjOOQIC 54 THE DIFFERENTIAL CALCULUS.
Ex.5. Ifttss*»-f-ax« + 5a?H-c; then ^=1.2.3.
Ex. 6. If « = sinar; then — = sin/* + ^Y cte* \ 2 / J'a?.
What to read after Elements of the Differential Calculus?
You can find similar books in the "Read Also" column, or choose other free books by Wesley Stokes Baker Woolhouse to read onlineMoreLess
To quickly assess the difficulty of the text, read a short excerpt:
differential coefficients of u mth respect to X ; or separately considering the numerators and denominators, du, d^u, d^u, &c. denote the first, second, third, &c. dif- ferentials of -M supposing dx to be constant, and dx, dx^, dx^, &c. as before, indicate c&r, {dx)^^ (dxy, &c. or powers of dx.
Example 1. Let m = a?" ; then — = nar"""*, dx ^ = n(n-l)ar«-2, ^ = «(n-l)(n-2)a?«-3,&c., ^ = «(n--l)(n^2)(n-3) 1 = 1.2.3 ... .«.
JEx. 2. Let tt = e* ; then by (26), du . d'^u . d^u dx * dx'^^ * dx^ ' Ex.... 3. Let u = cos X ; then — = — sin a? = cos ( a? + - j» d'^u / . 27r\ -pj ac — cos X = COS I J? -f — j» ^ = smj? = cosf 4? + — j, &C , d^u ( , nir\ J^d?. 4. Let M = e* cos a? ; then --- = e* cos J? — e' sirf 0! = c* (cos ^r — sin x) dx =:>/2c*C0s(j? + ^j £l=vj..{o»(.+;)-™(.+|)} = (V2)2e'cosU + -^j &c. &c.
j5 = (V-.)".-(. + --f> Digitized by VjOOQIC 54 THE DIFFERENTIAL CALCULUS.
Ex.5. Ifttss*»-f-ax« + 5a?H-c; then ^=1.2.3.
Ex. 6. If « = sinar; then — = sin/* + ^Y cte* \ 2 / J'a?.
What to read after Elements of the Differential Calculus?
You can find similar books in the "Read Also" column, or choose other free books by Wesley Stokes Baker Woolhouse to read onlineMoreLess
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