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Nuetrik [128]
3 years ago
6

Find derivative of the following problem ?

Mathematics
1 answer:
stepan [7]3 years ago
4 0
Let u = x.lnx, , w= x and t = lnx;  w' =1 ;  t' = 1/x

f(x) = e^(x.lnx) ; f(u) = e^(u); f'(u) = u'.e^(u)

let' find the  derivative u' of u
u = w.t
u'=  w't + t'w;  u' = lnx + x/x = lnx+1

u' = x+1 and f'(u) = ln(x+1).e^(xlnx)

finally the derivative of f(x) =ln(x+1).e^(x.lnx) + 2x
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3 years ago
Drag the expressions into the boxes to correctly complete the table. Polynomial Not a polynomial
uranmaximum [27]

The answer to the given question is as below:-

Polynomials:-

x³-7x²+9x-5x⁴-20

x⁵-5x⁴+4x³+2x-1

3x²-5x⁴+2x-12

Non-polynomial:-

x⁻5-5x⁻⁴+4x⁻³+2x⁻1-1

\dfrac{4}{x^4}+ \dfrac{3}{x^3}-\dfrac{2}{x^4}-1

\sqrt[4]{x} -\sqrt[3]{x} 4+\sqrt{x}-8x+16

<h3>What are polynomials?</h3>

A polynomial is a mathematical equation made up of indeterminates and coefficients and involves only addition, subtraction, multiplication, and non-negative integer exponentiation of variables. The exponents of the polynomials can not be irrational.

So the table will be formed as:-

Polynomials:-                            Non-polynomial:-        

x³-7x²+9x-5x⁴-20                     x⁻5-5x⁻⁴+4x⁻³+2x⁻1-1        

x⁵-5x⁴+4x³+2x-1                        \dfrac{4}{x^4}+ \dfrac{3}{x^3}-\dfrac{2}{x^4}-1

3x²-5x⁴+2x-12                           \sqrt[4]{x} -\sqrt[3]{x} 4+\sqrt{x}-8x+16

Therefore the polynomials and non-polynomials are shown in the table above.

To know more about polynomials follow

brainly.com/question/2833285

#SPJ1

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