Given: The function y = x²e7. Differentiate equation (1) with respect to x on both sides. - 4(re) dy dx dx Let u = x² and v = e7. Apply product rule and obtain as, *(fe#) =r4 ()+e4() (2) d dx dx dx The derivatives are found as, #(e) = (") (1-x-) = (-r") d dx dx %3D (x-2) 숲 (12) = 2x %3D Thus ouotion (2) hooomor

Q: A cat is falling from a branch. Its height t seconds after it fell is given by the function h(t) =…

A: We have given height  ht=-16t2+5 To get for what height cat was falling  Put t=0 h0=0+5 h0=5 height…

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A: Given f(x)=x3+15g(x)=x13

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A: Here We will show how in the step 2,  has come.

Q: Q3// Find without calculator: Csc-(V2)

A: Given problem is  :

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Q: 16. Condense the logarithms: a) 4logx - 2logx b) 5logx + 3logy + 2logy + 7logz

A: We can answer first question as per the honor policy. Please resubmit other question as well to now…

Q: shouldnt g^-1(f(x)) equal 3log2(X)-6 ? (the 2 after log is a subscript)

A: We will find the inverse function.

Q: Combine into a singel logarithm log(x-3)+log(x+3)-1/2log(x^2+9)

A: Given logarithm is  log(x-3)+log(x+3)-1/2log(x^2+9)

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Q: The identity of (a-b)^2+(a+b)^2 = 2(a^2+b^2) helped clean things up a lot. However, "ln" has to be…

A: Given,            The curve is rt=e2tcos2ti+4j+e2tsin2tk.To find : Reparametrize the curve with…

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A: Topic - exponents

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Q: ešlog (r-1)

A: Since you have asked multiple questions in single request so we will be answering only first…

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A: The given function is y=5x. We have to translate function 8 units to the right and 3 units downward.

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A: The formulas used are 1.∫dxax+b=1aln(ax+b)+c2.ddxxn=nxn-1

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A: Consider the given information: X"/X=T"/(a^2)T =-λ

Q: When do we use the Chain rule in derivates of exponential function

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