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Diamond plated differential calculus2/10/2024 \ Hintįirst verify that \(y\) solves the differential equation. +4\sin t\) is a solution to the initial-value problem Textbook content produced by OpenStax is licensed under a Creative Commons Attribution-NonCommercial-ShareAlike License. We recommend using aĪuthors: Gilbert Strang, Edwin “Jed” Herman Use the information below to generate a citation. Then you must include on every digital page view the following attribution: If you are redistributing all or part of this book in a digital format, Then you must include on every physical page the following attribution: If you are redistributing all or part of this book in a print format, Want to cite, share, or modify this book? This book uses theĬreative Commons Attribution-NonCommercial-ShareAlike License d d x ( sinh −1 x ) = 1 x 2 + 1 d d x ( sinh −1 x ) = 1 x 2 + 1ģ2. Nomads dont generally produce which means they need to, so they almost always live. d d x ( csch x ) = −csch x coth x d d x ( csch x ) = −csch x coth x Inverse Hyperbolic Functionsģ1. ![]() d d x ( coth x ) = − csch 2 x d d x ( coth x ) = − csch 2 xģ0. d d x ( cosh x ) = sinh x d d x ( cosh x ) = sinh xĢ9. d d x ( sech x ) = −sech x tanh x d d x ( sech x ) = −sech x tanh xĢ8. d d x ( tanh x ) = sech 2 x d d x ( tanh x ) = sech 2 xĢ7. d d x ( sinh x ) = cosh x d d x ( sinh x ) = cosh xĢ6. d d x ( log b x ) = 1 x ln b d d x ( log b x ) = 1 x ln b Hyperbolic FunctionsĢ5. d d x ( b x ) = b x ln b d d x ( b x ) = b x ln bĢ4. Exempel p versatt mening: Some problems concerning maxima and minima are studied in differential calculus, taught in college. d d x ( ln | x | ) = 1 x d d x ( ln | x | ) = 1 xĢ3. versttning av 'differential calculus' till svenska differentialkalkyl, differentialrkning r de bsta versttningarna av 'differential calculus' till svenska. A 'related rates'' problem is a problem in which we know one of the rates of change at a given instantsay, x dx/dt x d x / d t and. d d x ( e x ) = e x d d x ( e x ) = e xĢ2. Jump to exercises Suppose we have two variables x x and y y (in most problems the letters will be different, but for now let's use x x and y y) which are both changing with time. d d x ( csc −1 x ) = − 1 | x | x 2 − 1 d d x ( csc −1 x ) = − 1 | x | x 2 − 1 Exponential and Logarithmic FunctionsĢ1. d d x ( csc x ) = −csc x cot x d d x ( csc x ) = −csc x cot x Inverse Trigonometric Functionsġ5. d d x ( cot x ) = − csc 2 x d d x ( cot x ) = − csc 2 xġ4. d d x ( cos x ) = − sin x d d x ( cos x ) = − sin xġ3. d d x ( sec x ) = sec x tan x d d x ( sec x ) = sec x tan xġ2. ![]() d d x ( tan x ) = sec 2 x d d x ( tan x ) = sec 2 xġ1. d d x ( sin x ) = cos x d d x ( sin x ) = cos xġ0. d d x ( f ( x ) g ( x ) ) = g ( x ) f ′ ( x ) − f ( x ) g ′ ( x ) ( g ( x ) ) 2 d d x ( f ( x ) g ( x ) ) = g ( x ) f ′ ( x ) − f ( x ) g ′ ( x ) ( g ( x ) ) 2Ĩ. ![]() d d x ( f ( x ) − g ( x ) ) = f ′ ( x ) − g ′ ( x ) d d x ( f ( x ) − g ( x ) ) = f ′ ( x ) − g ′ ( x )ħ. d d x ( c f ( x ) ) = c f ′ ( x ) d d x ( c f ( x ) ) = c f ′ ( x )Ħ. d d x ( x n ) = n x n − 1, for real numbers n d d x ( x n ) = n x n − 1, for real numbers nĥ. d d x ( f ( x ) g ( x ) ) = f ′ ( x ) g ( x ) + f ( x ) g ′ ( x ) d d x ( f ( x ) g ( x ) ) = f ′ ( x ) g ( x ) + f ( x ) g ′ ( x )Ĥ. d d x ( f ( x ) + g ( x ) ) = f ′ ( x ) + g ′ ( x ) d d x ( f ( x ) + g ( x ) ) = f ′ ( x ) + g ′ ( x )ģ.
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