What is the derivative of $- e^{3 x^{2}}$ $-e^(3x^2)$ ?

Question

27977 views around the world

You can reuse this answer
Creative Commons License

Answer 1 · 2018-04-19T17:45:01

$\frac{d y}{d x} = - 6 x e^{3 x^{2}}$ $dy/dx=-6xe^(3x^2)$

By using chain rule for the function of function concept

$y = - e^{3 x}^2)$ $y=-e^(3x)^2)$

$y = - e^{t}$ $y=-e^t$

$\frac{d y}{d x} = - e^{t} \frac{d t}{d x}$ $dy/dx=-e^t(dt)/(dx)$

$t = 3 x^{2}$ $t=3x^2$

$t = 3 u$ $t=3u$

$u = x^{2}$ $u=x^2$

$\frac{d u}{d x} = 2 x$ $(du)/(dx)=2x$

$\frac{d t}{d x} = 3) d u \frac{)}{d x}$ $(dt)/(dx)=3)du)/(dx)$

$3 (d \frac{u}{d x} = 3 \times 2 x$ $3(du/(dx)=3xx2x$

$\frac{d t}{d x} = 3 \times 2 x$ $(dt)/(dx)=3xx2x$

$3 \times 2 x = 6 x$ $3xx2x=6x$

$\frac{d t}{d x} = 6 x$ $(dt)/(dx)=6x$

$\frac{d y}{d x} = - e^{t} \frac{d t}{d x}$ $dy/dx=-e^t(dt)/(dx)$

$\frac{d y}{d x} = - e^{3 x^{2}} (6 x)$ $dy/dx=-e^(3x^2)(6x)$

$\frac{d y}{d x} = - 6 x e^{3 x^{2}}$ $dy/dx=-6xe^(3x^2)$

What is the derivative of −e3x2-e^(3x^2)?