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Question
Function
Evaluate the derivative
Find the domain
Find the y-intercept
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f′(x)=−2863x6−21
Evaluate
f(x)=19−26x2×2x5−21x−17x3×21x4
Simplify
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Evaluate
19−26x2×2x5−21x−17x3×21x4
Multiply
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Multiply the terms
−26x2×2x5
Multiply the terms
−52x2×x5
Multiply the terms with the same base by adding their exponents
−52x2+5
Add the numbers
−52x7
19−52x7−21x−17x3×21x4
Multiply
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Multiply the terms
−17x3×21x4
Multiply the terms
−357x3×x4
Multiply the terms with the same base by adding their exponents
−357x3+4
Add the numbers
−357x7
19−52x7−21x−357x7
Subtract the terms
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Evaluate
−52x7−357x7
Collect like terms by calculating the sum or difference of their coefficients
(−52−357)x7
Subtract the numbers
−409x7
19−409x7−21x
f(x)=19−409x7−21x
Take the derivative of both sides
f′(x)=dxd(19−409x7−21x)
Use differentiation rule dxd(f(x)±g(x))=dxd(f(x))±dxd(g(x))
f′(x)=dxd(19)−dxd(409x7)−dxd(21x)
Use dxd(c)=0 to find derivative
f′(x)=0−dxd(409x7)−dxd(21x)
Calculate
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Calculate
dxd(409x7)
Use differentiation rule dxd(cf(x))=c×dxd(f(x))
409×dxd(x7)
Use dxdxn=nxn−1 to find derivative
409×7x6
Multiply the terms
2863x6
f′(x)=0−2863x6−dxd(21x)
Calculate
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Calculate
dxd(21x)
Use differentiation rule dxd(cf(x))=c×dxd(f(x))
21×dxd(x)
Use dxdxn=nxn−1 to find derivative
21×1
Any expression multiplied by 1 remains the same
21
f′(x)=0−2863x6−21
Solution
f′(x)=−2863x6−21
Show Solution
Testing for symmetry
Testing for symmetry about the origin
Testing for symmetry about the x-axis
Testing for symmetry about the y-axis
Not symmetry with respect to the origin
Evaluate
f(x)=19−26x22x5−21x−17x321x4
Simplify the expression
f(x)=19−409x7−21x
Rewrite the function using the appropriate notation
y=19−409x7−21x
To test if the graph of y=19−409x7−21x is symmetry with respect to the origin,substitute -x for x and -y for y
−y=19−409(−x)7−21(−x)
Simplify
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Evaluate
19−409(−x)7−21(−x)
Multiply the terms
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Evaluate
−409(−x)7
Rewrite the expression
−409(−x7)
Multiply the numbers
409x7
19+409x7−21(−x)
Multiply the numbers
19+409x7+21x
−y=19+409x7+21x
Change the signs both sides
y=−19−409x7−21x
Solution
Not symmetry with respect to the origin
Show Solution
Graph
