Question

differentiate.
f(x)=10e^{x}
f(x)=\square

Explanation:

Step1: Apply the constant - multiple rule

The constant - multiple rule states that if \(y = cf(x)\), then \(y^\prime=c\cdot f^\prime(x)\). Here \(c = 10\) and \(f(x)=e^{x}\), so \(f^\prime(x)=10\cdot\frac{d}{dx}(e^{x})\).

Step2: Use the derivative formula for \(e^{x}\)

The derivative of \(e^{x}\) with respect to \(x\) is \(e^{x}\), i.e., \(\frac{d}{dx}(e^{x})=e^{x}\).
So \(f^\prime(x)=10\cdot e^{x}\).

Answer:

\(10e^{x}\)