Solution: Derivative Power Rule #3
Solution: Derivative Power Rule #3
Find the derivative [latex]P'(x)[/latex] of:
[latex]\Large{P(x) = 6x^6-2x^4+5x^2-1}[/latex]
Step 1:
We can use the derivative power rule to find the derivative of the given function. We have:
[latex]\large{P'(x) = 6(6)x^{6-1}-2(4)x^{4-1}+5(2)x^{2-1}}[/latex]
Notice that we brought down the exponent, and subtracted the exponent by 1 for each term.
Step 2:
Now, after simplifying, we have:
[latex]\large{P'(x) = 36x^5-8x^3+10x}[/latex]
This is our final answer for the derivative.
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Solution: Derivative Power Rule #3
Find the derivative [latex]P'(x)[/latex] of:
[latex]\Large{P(x) = 6x^6-2x^4+5x^2-1}[/latex]
Step 1:
We can use the derivative power rule to find the derivative of the given function. We have:
[latex]\small{P'(x) = 6(6)x^{6-1}-2(4)x^{4-1}+5(2)x^{2-1}}[/latex]
Notice that we brought down the exponent, and subtracted the exponent by 1 for each term.
Step 2:
Now, after simplifying, we have:
[latex]\large{P'(x) = 36x^5-8x^3+10x}[/latex]
This is our final answer for the derivative.
Solution Complete!
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Solution: Derivative Power Rule #1
Find the derivative [latex]f'(x)[/latex] of:
[latex]\Large{f(x) = 5x^3+2x^2-7x+1}[/latex]
Step 1:
We can use the derivative power rule to find the derivative of the given function. We have:
[latex]\small{f'(x) = 5(3)x^{3-1}+2(2)x^{2-1}-7(1)x^{1-0}}[/latex]
Notice that we brought down the exponent, and subtracted the exponent by 1 for each term.
Step 2:
Now, after simplifying, we have:
[latex]\large{f'(x) = 15x^2+4x-7}[/latex]
This is our final answer for the derivative.
Solution Complete!
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