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Solving Calculus Problems

 The problems in calculus varies widely with a range of different ways of solving the calculus problems such as using sum rule,product rule,quotient rule,by first principle method ,chain rule .By using these methods we will be able to solve any given function.The problems are subject to different levels such as inverse trigonometric problems,substitution based, parametric equations .There are certain procedures and  standards to solve the calculus problems.

Help Solving Calculus Problems

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To start with solving problems on calculus let us put down few  results of derivatives of algebraic ,trigonometric,exponential,and logarithmic functions.
1.$\frac{\mathrm{d} (sinx)}{\mathrm{d} x}$=cosx
2.$\frac{\mathrm{d} (cosx)}{\mathrm{d} x}$= -sinx
3.$\frac{\mathrm{d} (tanx)}{\mathrm{d} x}$=sec2x
4.$\frac{\mathrm{d} (secx)}{\mathrm{d} x}$=secxtanx
5.$\frac{\mathrm{d} (cosecx)}{\mathrm{d} x}$=-cosecxcotx
6.$\frac{\mathrm{d} (cotx)}{\mathrm{d} x}$=-cosec2x
7.$\frac{\mathrm{d} (e^{ax})}{\mathrm{d} x}$ = aeax
8.$\frac{\mathrm{d} (logx)}{\mathrm{d} x}$=1/x
we shall use the above results in solving the problems based on calculus.
Example 1
Find the derivative of  sinx+cosx.
step1:$\frac{\mathrm{d} (sinx+cosx)}{\mathrm{d} x}$=cosx-sinx.
solution :cosx-sinx.
Example 2
Find the derivative of  x2+ 3sinx- tanx
step1:
$\frac{\mathrm{d} ( x2+ 3sinx- tanx)}{\mathrm{d} x}$=2x+3cosx-sec2x.
solution :2x+3cosx-sec2x.
Example 3
Find the derivative of  x2logx.
In this case we use Product rule were u= x2and v=logx.
Formula
$u\frac{\mathrm{d} v}{\mathrm{d} x}+v\frac{\mathrm{d} u}{\mathrm{d} x}$
Step1 : $x\frac{\mathrm{d}logx}{\mathrm{d} x}+logx\frac{\mathrm{d} x}{\mathrm{d} x}$
Step2 : x (1/x) + logx (1). This is from the formula used in the above result.
Step3 : 1+logx.
Solution : 1+logx
Example 4
Differentiate logx/x
In this case we can use Quotient rule but we try to use product rule alternatively  and solve
Formula
$u\frac{\mathrm{d}v}{\mathrm{d} x}+v\frac{\mathrm{d} u}{\mathrm{d} x}$
step1:$(1/x)\frac{\mathrm{d}logx}{\mathrm{d} x}+logx\frac{\mathrm{d} (1/x)}{\mathrm{d} x}$
step2:(1/x)(1/x) + logx/x
step3: 1/x2+ logx/x.
Example 5
Differentiate cosecx-x2+4tanx.
Formulae
$\frac{\mathrm{d} u}{\mathrm{d} x}+\frac{\mathrm{d} v}{\mathrm{d} x}+\frac{\mathrm{d} w}{\mathrm{d} x}$
step 1 :$ \frac{\mathrm{d} cosecx}{\mathrm{d} x}-\frac{\mathrm{d} x}{\mathrm{d} x}+4\frac{\mathrm{d}tanx }{\mathrm{d} x}$
step 2: -cosecxcotx-2x+4sec2x.
solution :-cosecxcotx-2x+4sec2x.