find the derivative of (y = 15cdot14^{x}-x^{6}).\n(\frac{dy}{dx}=)

Explanation:

Step1: Apply sum - difference rule

The derivative of a sum/difference of functions is the sum/difference of their derivatives. So, $\frac{dy}{dx}=\frac{d}{dx}(15\cdot14^{x})-\frac{d}{dx}(x^{6})$.

Step2: Derivative of $a\cdot b^{x}$

The derivative of $a\cdot b^{x}$ with respect to $x$ is $a\cdot b^{x}\ln(b)$. For $a = 15$ and $b = 14$, $\frac{d}{dx}(15\cdot14^{x})=15\cdot14^{x}\ln(14)$.

Step3: Derivative of $x^{n}$

The power - rule states that $\frac{d}{dx}(x^{n})=nx^{n - 1}$. For $n = 6$, $\frac{d}{dx}(x^{6})=6x^{5}$.

Answer:

$15\cdot14^{x}\ln(14)-6x^{5}$