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If g(x)=(log log x)/x . Evaluate d/dx[g(x)].
8xlnx+4x
(x)/(x2)
(2x)/(x2)
If g(x)=(x+5)e2xg\left(x\right)=\frac{\left(x+5\right)}{e^{2x}}g(x)=e2x(x+5) .Evaluate d/dx[g(x)].
2ex2e^x2ex
(ex+(x+5)ex)e2x\frac{\left(e^x+\left(x+5\right)e^x\right)}{e^{2x}}e2x(ex+(x+5)ex)
(ex−(x+5)ex)e2x\frac{\left(e^x-\left(x+5\right)e^x\right)}{e^{2x}}e2x(ex−(x+5)ex)
If f(x)=1+x1−xf\left(x\right)=\frac{\sqrt{1+x}}{\sqrt{1-x}}f(x)=1−x1+x . Evaluate d/dx[f(x)].
5(1−x)1−x2\frac{5}{\left(1-x\right)\sqrt{1-x^2}}(1−x)1−x25
1(1−x)1−x2\frac{1}{\left(1-x\right)\sqrt{1-x^2}}(1−x)1−x21
2(1−x)1−x2\frac{2}{\left(1-x\right)\sqrt{1-x^2}}(1−x)1−x22
If g(x)=cosxxg\left(x\right)=\frac{\cos x}{x}g(x)=xcosx . Evaluate d/dx[g(x)].
(−xsinx+cosx)x2\frac{\left(-x\sin x+\cos x\right)}{x^2}x2(−xsinx+cosx)
(xsinx+cosx)x2\frac{\left(x\sin x+\cos x\right)}{x^2}x2(xsinx+cosx)
−sinx+1x-\sin x+\frac{1}{x}−sinx+x1
If g(x)=x2x+1g\left(x\right)=\frac{x^2}{x+1}g(x)=x+1x2 . Evaluate d/dx[g(x)].
(x2+x)(x+1)2\frac{\left(x^2+x\right)}{\left(x+1\right)^2}(x+1)2(x2+x)
(x2+2x)(x+1)2\frac{\left(x^2+2x\right)}{\left(x+1\right)^2}(x+1)2(x2+2x)
(x2+2)(x+1)2\frac{\left(x^2+2\right)}{\left(x+1\right)^2}(x+1)2(x2+2)
If f(x)=(x+2)/(2-x). Evaluate d/dx[f(x)].
2/(2-x)2
2/(2+x)2
4/(2-x)2
If f(x)=(x3)/(4x). Evaluate d/dx[f(x)].
2x
2x+2
x/2
If g(x)=(x+5)(5−x)g\left(x\right)=\frac{\left(x+5\right)}{\left(5-x\right)}g(x)=(5−x)(x+5) . Evaluateddx[g(x)]\frac{d}{dx}\left[g\left(x\right)\right]dxd[g(x)] .
20(20−x)2\frac{20}{\left(20-x\right)^2}(20−x)220
10(5−x)2\frac{10}{\left(5-x\right)^2}(5−x)210
10(20−x)2\frac{10}{\left(20-x\right)^2}(20−x)210
If f(x)=(x+a)/(a-x). Evaluate d/dx[f(x)].
2a/(a-x)2
2a/(a+x)2
a/(a-x)2
If f(x)=(2x-3)/(2x+1). Evaluate d/dx[f(x)].
4/(2x+1)2
8/(x+1)2
8/(2x+1)2
It is done.