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