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Divide $\pi $ by $3$
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$derivdef\left(80+90\cos\left(\frac{\pi}{3}x\right)\right)$
Learn how to solve problems step by step online. Find the derivative of 80+90cos(pi/3x) using the definition. Divide \pi by 3. Find the derivative of 80+90\cos\left(\frac{\pi}{3}x\right) using the definition. Apply the definition of the derivative: \displaystyle f'(x)=\lim_{h\to0}\frac{f(x+h)-f(x)}{h}. The function f(x) is the function we want to differentiate, which is 80+90\cos\left(\frac{\pi}{3}x\right). Substituting f(x+h) and f(x) on the limit, we get. Multiply the single term \frac{\pi}{3} by each term of the polynomial \left(x+h\right). Multiply the single term -1 by each term of the polynomial \left(80+90\cos\left(\frac{\pi}{3}x\right)\right).