Mathematics
语言:中文
Language:English

current location:Derivative function > Derivative function calculation history > Answer
    There are 1 questions in this calculation: for each question, the 4 derivative of x is calculated.
    Note that variables are case sensitive.
\[ \begin{equation}\begin{split}[1/1]Find\ the\ 4th\ derivative\ of\ function\ {(2x - 4)}^{5}\ with\ respect\ to\ x:\\\end{split}\end{equation} \]\[ \begin{equation}\begin{split}\\Solution:&\\ &Primitive\ function\ = 32x^{5} - 320x^{4} + 1280x^{3} - 2560x^{2} + 2560x - 1024\\&\color{blue}{The\ first\ derivative\ function:}\\&\frac{d\left( 32x^{5} - 320x^{4} + 1280x^{3} - 2560x^{2} + 2560x - 1024\right)}{dx}\\=&32*5x^{4} - 320*4x^{3} + 1280*3x^{2} - 2560*2x + 2560 + 0\\=&160x^{4} - 1280x^{3} + 3840x^{2} - 5120x + 2560\\\\ &\color{blue}{The\ second\ derivative\ of\ function:} \\&\frac{d\left( 160x^{4} - 1280x^{3} + 3840x^{2} - 5120x + 2560\right)}{dx}\\=&160*4x^{3} - 1280*3x^{2} + 3840*2x - 5120 + 0\\=&640x^{3} - 3840x^{2} + 7680x - 5120\\\\ &\color{blue}{The\ third\ derivative\ of\ function:} \\&\frac{d\left( 640x^{3} - 3840x^{2} + 7680x - 5120\right)}{dx}\\=&640*3x^{2} - 3840*2x + 7680 + 0\\=&1920x^{2} - 7680x + 7680\\\\ &\color{blue}{The\ 4th\ derivative\ of\ function:} \\&\frac{d\left( 1920x^{2} - 7680x + 7680\right)}{dx}\\=&1920*2x - 7680 + 0\\=&3840x - 7680\\ \end{split}\end{equation} \]





Your problem has not been solved here? Please take a look at the  hot problems !


Return