Final Answer
$1680x^{5}$
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Step-by-step Solution
Problem to solve:
$\frac{d}{dx}\left(\frac{d}{dx}\left(\frac{d}{dx}\left(5x^8\right)\right)\right)$
Specify the solving method
1
The derivative $\frac{d}{dx}\left(5x^8\right)$ results in $40x^{7}$
$\frac{d}{dx}\left(\frac{d}{dx}\left(40x^{7}\right)\right)$
Learn how to solve differential calculus problems step by step online.
$\frac{d}{dx}\left(\frac{d}{dx}\left(40x^{7}\right)\right)$
Learn how to solve differential calculus problems step by step online. Find the derivative of (d/dx)((d/dx)(5x^8)). The derivative \frac{d}{dx}\left(5x^8\right) results in 40x^{7}. The derivative \frac{d}{dx}\left(40x^{7}\right) results in 280x^{6}. The derivative of a function multiplied by a constant (280) is equal to the constant times the derivative of the function. The power rule for differentiation states that if n is a real number and f(x) = x^n, then f'(x) = nx^{n-1}.
Final Answer
$1680x^{5}$