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Higher mathematics problems: on the problem of derivative What is the definition of the second derivative of F (x) at x0?
f''(x0)=lim h->0 [f'(x0+h)-f'(x0)]/h .
High number problem derivation!
y=(sinx/x)+(x/sinx)
y=(1-x²）tanxlnx
1. SiNx / X derivative, this is fractional derivative, the following becomes x-square, the above first differentiates the above SiNx, the following X does not derive, minus SiNx does not derive x derivative, we can get (cosx * x-sinx) / (x ^ 2). The following is similar. The final result is (cosx * x-sinx) / (x ^ 2) + (sinx-x * cosx) / (SiNx ^ 2)
2. Look at the derivative 1-x & sup2 of two formulas multiplication; multiply tanxlnx, the front leader does not lead to - 2xtanxlnx, plus the front leader leads to 1-x & sup2; (tanxlnx) after the front leader, the front leader does not lead to LNX / (cosx) square, plus the back leader does not lead to TaNx / X. finally, we get - 2xtanxlnx + 1-x & sup2; (LNX / cosx + TaNx / x)
Derivation of (cosx & sup2;) under y = radical
-Xtan (X & sup2;) under the radical (cosx & sup2;)
Y = (cosx & sup2;)] '= [(cosx & sup2;) ^ (1 / 2)]' = (1 / 2) × (cosx & sup2;) ^ (- 1 / 2) × (cosx & sup2;) '= (1 / 2) × (cosx & sup2;) ^ (- 1 / 2) × (- SiNx & sup2;) × (X & sup2;)' = (1 / 2) × (cosx & sup2;) ^ (- 1 / 2) × (- SiNx & sup2;) ×
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