## Mixed Differentiation Problems 1

Differentiation is used to analyze the properties such as intervals of increase, decrease, local maximum, local minimum of quadratic functions. Examples with solutions and exercises with

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## Calculus I

Solve this linear differential equation. \displaystyle x\dfrac {dy} {dx}-y=x^ {2}\sin (x) xdxdy −y = x2sin(x) \displaystyle y=-y\cos x+c y = −ycosx+c. \displaystyle y=-x\cos y+C y = −xcosy +C.

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Mathematics is the study of numbers, shapes and patterns. It is used in everyday life, from counting and measuring to more complex problems. There are many different types of mathematical questions, from simple addition and subtraction to more complex calculus.

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Solution : the distance x meters traveled by a vehicle in time t seconds. x = 20 t - (5/3)t 2. To find the speed of the vehicle, differentiate it with respect to t dx/dt = 20 (1) - (5/3)(2t) = 20 - (10 t/3)

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## List of Derivative Problems

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## SOLUTIONS TO 18.01 EXERCISES

For problems 1 – 3 use logarithmic differentiation to find the first derivative of the given function. f (x) = (5 −3x2)7 √6x2+8x −12 f ( x) = ( 5 − 3 x 2) 7 6 x 2 + 8 x − 12 Solution. y =
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