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Step-by-step Solution
How should I solve this problem?
- Find the derivative using the definition
- Integrate by partial fractions
- Product of Binomials with Common Term
- FOIL Method
- Integrate by substitution
- Integrate by parts
- Integrate using tabular integration
- Integrate by trigonometric substitution
- Weierstrass Substitution
- Prove from LHS (left-hand side)
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Take $\frac{\pi }{2}$ out of the fraction
Learn how to solve definition of derivative problems step by step online.
$derivdef\left(\sin\left(\frac{\pi}{2}x\right)\right)$
Learn how to solve definition of derivative problems step by step online. Find the derivative of sin((pix)/2) using the definition. Take \frac{\pi }{2} out of the fraction. Find the derivative of \sin\left(\frac{\pi}{2}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 \sin\left(\frac{\pi}{2}x\right). Substituting f(x+h) and f(x) on the limit, we get. Multiply the single term \frac{\pi}{2} by each term of the polynomial \left(x+h\right). Using the sine of a sum formula: \sin(\alpha\pm\beta)=\sin(\alpha)\cos(\beta)\pm\cos(\alpha)\sin(\beta), where angle \alpha equals \frac{\pi}{2}x, and angle \beta equals \frac{\pi}{2}h.