Question

急.若函数f(x)=(e^x)cos x,则此函数图像在（0,f(0)）处的切线的斜率角为

Answer 1

f(x)=(e^x)cos x

f'(x) = (e^x) * (cos x)' + (e^x)' * cos x = -e^x * sin x + e^x * cos x

f'(0) b = -e^0 * sin 0 + e^0 * cos 0 = -1 *0 + 1 *1 = 1

函数图像在（0,f(0)）处的切线的斜率k=1

斜率角=arc tan 1 = 45°