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Prove using the definition of derivative, that if $ f(x) = $ cos $ x, $ then $ f'(x) = - $ sin $ x. $
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Calculus 1 / AB
Derivatives of Trigonometric Functions
March 12, 2022
Missouri State University
Oregon State University
University of Nottingham
In mathematics, a derivative is a measure of how a function changes as its input changes. Loosely speaking, a derivative can be thought of as how much one quantity is changing in response to changes in some other quantity; for example, the derivative of the position of a moving object with respect to time is the object's velocity. The concept of a derivative developed as a way to measure the steepness of a curve; the concept was ultimately generalized and now "derivative" is often used to refer to the relationship between two variables, independent and dependent, and to various related notions, such as the differential.
In mathematics, a differentiation rule is a rule for computing the derivative of a function in one variable. Many differentiation rules can be expressed as a product rule.
Prove, using the definitio…
Use the definition of a de…
Find the derivative of the…
Use the definition of deri…
It's clear, so enumerated here. So we have the definition of the derivative. So are given is F of X is equal to co sign a X, then the derivative this equal to limit Does age approaches. Cerro Rico Signed Put X plus inch miners Co sign of X well over a tch. This gives us the limit. Thus each approaches Sarah Co Sign of X Times Coastline of H minus Sign of X times Sign of H minus Co sign of X over h excuse This limit Those age approaches Ciro her co sign Guns Co sign of age minus co Sign of X minus Sign of X times sign of H all over h And then this is Clement. That's H approaches Ciro for co sign of X Times Co sign of H minus one over H minus. Sign of X of sign of H over each. This gives us co sign of X times delimit as each approaches Ciro for co signed of H minus one over H minus sign of pecs for the limit as each approaches zero the sign of a TSH over change. So this becomes zero and this becomes one and this gives us a negative sign of X
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