设$f'(x)=\sin x$且$f(0)=-1$，则$f(x)$的一个原函数为
A: $1+\sin x$.
B: $1-\sin x$.
C: $1+\cos x$.
D: $1-\cos x$.
A: $1+\sin x$.
B: $1-\sin x$.
C: $1+\cos x$.
D: $1-\cos x$.
举一反三
- 若$f(x)$的导函数是$\sin x$，则下列函数中是$f(x)$原函数的为( ). A: $1+\sin x$ B: $1-\cos x$ C: $1+\cos x$ D: $1-\sin x$
- 17e0b849d3a4a3b.jpg,计算[img=19x34]17e0ab14a855463.jpg[/img]的实验命令为（ ）. A: syms x; f=diff((1+sin(x)^2)/cos(x),1)f=2*sin(x) + (sin(x)*(sin(x)^2 + 1))/cos(x)^2 B: f=diff((1+sinx^2)/cosx,1)f=1/2/x^(1/2)/(1-x)^(1/2) C: syms x;f=diff((1+sinx^2)/cosx,1)f=2*sin(x) + (sin(x)*(sin(x)^2 + 1))/cos(x)^2
- 求函数$f(x)=x^{\sin x}$的导数 A: $x^{\cos x}$ B: $\sin (x) x^{\sin (x) -1}$ C: $x^{\sin x}(\cos x\ln x+\frac{\sin x}{x})$ D: $x^{\sin x}(\sin x\ln x+\frac{\cos x}{x}$
- 求函数[img=107x38]17da6537b12a2e0.png[/img]的导数； ( ) A: 2*x*sin(1/x) - sin(1/x) B: 2xsin(1/x) - cos(1/x) C: 2*x*sin(1/x) - cos(1/x) D: 2*x*cos(1/x) - cos(1/x)
- 将函数\(f(x)=\sin^4 x\)展开成Fourier级数为 ____ . A: \(f(x) = \frac{3}{8}-\frac{1}{2}\cos 2x +\frac{1}{8}cos 4x\) B: \(f(x) = \frac{1}{4}-\frac{1}{2}\cos x +\frac{3}{8}cos 4x\) C: \(f(x) = \frac{1}{4}-\frac{1}{2}\sin 2x -\frac{3}{8}cos 4x\) D: \(f(x) = \frac{3}{8}-\frac{1}{2}\sin x -\frac{1}{8}cos 4x\)