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**keemariee** simplify: exp(a)^-1 * exp (b)^2/exp(5c)

**Iso: You just need to know basic laws of exponentiation. Like $\displaystyle e^x e^y = e^{x+y}$ and **$\displaystyle e^{-x} = \frac1{e^x}$

So your question reads $\displaystyle (e^{a})^{-1} {(e^b)}^2/e^{5c} = e^{-a + 2b -5c}$

calculate: d/dx exp(xsin(x))

**Iso: Use chain rule:**

$\displaystyle \frac{d(e^{x \sin x})}{dx} = e^{x\sin x} \frac{d(x\sin x)}{dx}=....$

So can you continue now?

calculate: (integral)xexp(x^2-3)dx

**Iso: Substitute $\displaystyle u = x^2 - 3$, so that $\displaystyle du = 2x \, dx$**

$\displaystyle \boxed{\int x e^{x^2-3}\,dx = \frac12 \int e^{u}\,du = \frac{e^{x^2 - 3}}{2}}$

find the exponential function f(x)=a^x whose graph goes through point 5, 1/32. a=???

find the exponential funtion f(x)=Ca^x whose graph goes through points (0,2) and (4,32). a=??? C=???