Sin 2X 1 Cosx. PDF filex 1 x2 2x x3 3×2 xn any constant n nxn−1 ex ex ekx kekx lnx = log e x 1 x sinx cosx sinkx kcoskx cosx −sinx coskx −ksinkx tanx = sinx cosx sec2 x tankx ksec2 kx cosecx = 1 sinx −cosecxcot x secx = 1 cosx secxtanx cotx = cosx sinx −cosec2x sin− 1x √ 1−x2 cos−1 x √−1 1−x2 tan−1 x 1 1+x2 coshx sinhx sinhx coshx tanhx sech2x sechx −sechxtanhx cosechx −cosechxcothx.
Balbharati solutions for Mathematics and Statistics 1 (Arts and Science) 11th Standard Maharashtra State Board chapter 3 (Trigonometry 2) include all questions with solution and detail explanation This will clear students doubts about any question and improve application skills while preparing for board exams The detailed stepbystep solutions will help you.
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PDF file37= sec f(x) xsin(3x) 38 f(x) = (x−1)3 x3)(x+ 4 39= log f(x) 5 (3×2 +4x) In problems 40 – 42 find dy dx Assume y is a differentiable function of x 40 3y = xe5y 41y x +y2 +x3 = 7 42 siny y2 +1 = 3x If f and g are differentiable functions such that f(2) = 3 f′(2) = −1 f′(3) = 7 g(2) = −5 and g′(2) = 2 find the numbers indicated in problems 43 – 48 43 (g.
MATH 171 Derivative Worksheet Differentiate these for fun
f’’(x) = 2a (x 11) f’’(x) = 2a Example 3 What is the second derivative of sinx + x/2? Solution First derivative Step 1 Apply the derivative f’(x) = d/dx (sinx + x/2) Step 2 Apply the Sum rule f’(x) = d/dx(sinx) + d/dx(x/2) Step 3 Take out the constant f’(x) = cosx + (½)d/dx(x) f’(x) = cosx + ½ Second derivative.
Second Derivative Calculator With steps
By changing variables integration can be simplified by using the substitutions x=a\sin(\theta) x=a\tan(\theta) or x=a\sec(\theta) Once the substitution is made the function can be simplified using basic trigonometric identities.
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PDF file(e +sin )d 77 Z 2e e cosx 1 x dx ANSWERS Inde nite integrals 1 2×2 +3x+C 2 4×3 3 4×2 +x+C 3 3t3 2t2 +3t+C 4 t4 2 t3 3 + 3t2 2 7t+C 5 z 2 2 +3z 21 +C 6 4z 6 6 + 7z 3 3 + z2 2 +C 7 2u3=2 +2u1=2 +C 8 2u5=2 5 + u 1 2 +5u+C 9 8v9=4 9 + 24v5=4 5 v 3 + C 10 v6 2 3v8=3 8 +C 11 3×3 3×2 +x+C 12 x3 3 2x x 41 cot1 +C 13 2×3 3 + 3×2 2 +C 14 2×3 13×2 2 5x+C 15 24×5=3 5.