File name: Standard derivatives pdf
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Integrate the partial fraction omposition (P.F.D.). term(s) in the omposition according to the following table. Factor of TABLE OF DERIVATIVES FUNCTION DERIVATIVE Ccx c x aaxsinx cosx cosx sinx tanx (secx)2 secx secxtanx e xe lnjxjx ax (lna)ax log b x(lnb)x sinhx coshx coshx sinhx tanhx (sechx)2 arcsinxpx2 arccosxpx2 arctanxx2 +1 Z x a f(t)dt f(x) Multiply by current power. TABLE OF DERIVATIVES FUNCTION DERIVATIVE Ccx c x aaxsinx cosx cosx sinx tanx (secx)2 secx secxtanx e xe lnjxjx ax (lna)ax log b x(lnb)x sinhx coshx coshx Okay, so we know the derivatives of constants, of x, and of x2, and we can use these (together with the linearity of the derivative) to compute derivatives of linear and DERIVATIVES & INTEGRALS Jordan Paschke Derivatives Here are a bunch of derivatives you should probably know. We highly recommend practicing with them (or Calculus, section The Derivative. We highly recommend practicing with them (or creating ashcards for them) and looking at them occasionally until they are burned into your memory. Let’s start with an example: d DERIVATIVES & INTEGRALS Jordan Paschke Derivatives Here are a bunch of derivatives you should probably know. We now take the idea of section (the slope of a curve at a point P) and treat it more formally. function: f(x) derivative: f0(x) x aaxsin(x) cos(x) cos(x) sin(x) tan(x) sec2(x) cot(x How can we do this? Addto power Okay, so we know the derivatives of constants, of x, and of x2, and we can use these (together with the linearity of the derivative) to compute derivatives of linear and quadratic functions. For each factor in the denominator we get. Given a function f(x), the first derivative these results together and construct a table of standard derivatives which you can consult as the need arisesA Table of Derivatives Commonly occurring functions and their Table of derivatives Introduction This leaflet provides a table of common functions and their derivativesThe table of derivatives y = f(x) dy dx = f′(x) k, any constantxxx xx2 xn, any constant n nxn−1 ex ex ekx kekx lnx = log e xx sinx cosx sinkx kcoskx cosx −sinx coskx −ksinkx tanx = sinx cosx sec2 x tankx ksec2 kx Q(x) then factor the denominator. as completely as possible and find the partial fraction omposition of the rational expression. To compute the derivatives of all polynomials, we’d need to know the derivatives of xn for higher n.
