若函数f(x)＝x³－f ′(－1)·x²＋x＋5，则f ′(1)＝________.

已知f(x)＝ax³＋3x²＋2，若f ′(－1)＝4，则a的值为

________．

若函数f(x)＝e^xsinx，则此函数图像在点(4，f(4))处的切线的倾斜角为(　　)

A.　　　　                                               B．0

C．钝角　　　　                                          D．锐角

已知点P在曲线f(x)＝x⁴－x上，曲线在点P处的切线平行于直线3x－y＝0，则点P的坐标为(　　)

A．(0,0)                                                        B．(1,1)

C．(0,1)                                                        D．(1,0)

已知曲线y＝x⁴＋ax²＋1在点(－1，a＋2)处切线的斜率为8，则a＝(　　)

A．9                                                             B．6

C．－9                                                          D．－6

设f₀(x)＝sinx，f₁(x)＝f ′₀(x)，f₂(x)＝f ′₁(x)，…，f_n＋1(x)＝f ′_n(x)，n∈N，则f_{2 015}(x)等于(　　)

A．sinx                                                         B．－sinx

C．cosx                                                        D．－cosx

曲线y＝e^x在点A(0,1)处的切线斜率为(　　)

A．1                                                             B．2

C．e                                                             D.

若函数f(x)＝x²＋bx＋c的图像的顶点在第二象限，则函数f ′(x)的图像是(　　)

已知f(x)＝xlnx，若f ′(x₀)＝2，则x₀＝(　　)

A．e²                                                            B．e

C.                                                          D．ln2

下列求导数运算正确的是(　　)

A．(x＋)′＝1＋                                 B．(log₂x)′＝

C．(3^x)′＝3^xlog₃e                                         D．(x²cosx)′＝－2xsinx