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Derivative of tan(x) using the quotient rule, done in 1 minute!
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In this video, we will find the derivative of the tangent function using the quotient rule. The derivative with respect to x of tan(x) is obtained by differentiating the numerator and denominator separately. We apply the quotient rule (low d high - high d low) / (low^2).
1. Let the numerator be sin(x) and the denominator be cos(x).
2. Apply the quotient rule (cos(x) * d/dx[sin(x)] - sin(x) * d/dx[cos(x)]) / (cos^2(x)).
3. Differentiate sin(x) to get cos(x), and differentiate cos(x) to get -sin(x).
4. Substitute the values (cos(x) * cos(x) - sin(x) * (-sin(x))) / (cos^2(x)).
5. Simplify (cos^2(x) + sin^2(x)) / (cos^2(x)).
6. Use the trigonometric identity sin^2(x) + cos^2(x) = 1.
7. Substitute the identity 1 / (cos^2(x)).
8. Recall that sec^2(x) = 1 / cos^2(x).
9. Final result sec^2(x).
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1. Let the numerator be sin(x) and the denominator be cos(x).
2. Apply the quotient rule (cos(x) * d/dx[sin(x)] - sin(x) * d/dx[cos(x)]) / (cos^2(x)).
3. Differentiate sin(x) to get cos(x), and differentiate cos(x) to get -sin(x).
4. Substitute the values (cos(x) * cos(x) - sin(x) * (-sin(x))) / (cos^2(x)).
5. Simplify (cos^2(x) + sin^2(x)) / (cos^2(x)).
6. Use the trigonometric identity sin^2(x) + cos^2(x) = 1.
7. Substitute the identity 1 / (cos^2(x)).
8. Recall that sec^2(x) = 1 / cos^2(x).
9. Final result sec^2(x).
Thank you for watching! Don't forget to like and subscribe for more math videos. See you in the next one!
Please visit our Merch Stores and help support the spreading of knowledge:)
Our T-Shirt Merch:
Our Amazon Store for Awesome Merch too: