Expand each function (using the appropiate technique/formula) Compute the derivative

Susan Nall 2021-12-12 Answered
Expand each function (using the appropiate technique/formula) Compute the derivative of the expanded function by applying the differentiation rules
f(x)=(x+5)2
f(x)=(4x23)2
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Expert Answer

kaluitagf
Answered 2021-12-13 Author has 38 answers
Step 1: To determine
Derivative of the given functions by expanding them:
1) f(x)=(x+5)2
2) f(x)=(4x23)2
Step 2: Formula used
1. (x+y)2=x2+2xy+y2
2. (xy)2=x2xy+y2
3. ddx(xn)=nxn1
Step 3: Solution
Consider the given function:
f(x)=(x+5)2
Using formula, the expanded function is given by:
f(x)=x2+2.x.5+52
f(x)=x2+10x+25
Differentiating the above function with respect to x, we get,
df(x)dx=ddx(x2+10x+25)
df(x)dx=ddx(x2)+ddx(10x)+ddx(25)
df(x)dx=2x+10(1)+0
df(x)dx=2x+10
Hence, the derivative of the given function is dfdx=2x+10
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Chanell Sanborn
Answered 2021-12-14 Author has 41 answers
Step 4
Consider the given function:
f(x)=(4x23)2
Using formula, the expanded function is given by:
f(x)=(4x2)22.(4x2)(3)+32
f(x)=16x424x2+9
Differentiating the above function with respect to x, we get,
df(x)dx=ddx(16x424x2+9)
df(x)dx=ddx(16x4)+ddx(24x2)+ddx(9)
df(x)dx=16ddx(x4)24ddx(x2)+ddx(9)
df(x)dx=16(4x3)24(2x)+(0)
df(x)dx=64x348x
Hence, the derivative of the given function is dfdx=64x348x
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