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they want to verify this formula by using differentiation.
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So what we want to do is think the derivative
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of this function on the right hand side and see
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if we get what we are integrating here. So
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go ahead and apply are derivative to the right hand
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side. So derivative of negative three X plus five
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raised the negative 1/3 plus C. Now the derivative
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is a linear operator, so we can distribute it
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across the plus and minus as well as Paul.
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Any Constance. So we can rewrite this us negative
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1/3 and then taking the integral of three x plus
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five recent negative first power is going to be power
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and changeable. So power rule, her says.
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We subtract one from Powers. There's gonna be negative
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, too now and then we multiply with Clarence and
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different color negative, too, and we multiply by
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the whole powers that be negative one and then change
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Will says we have to take a trip of our
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inside function, and the derivative of three X plus
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five would just be three multiplied by three. And
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it would take the derivative of a constant. See
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, that's just zero. Let's go ahead and clean
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this up a little bit. So first thes negatives
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council out with each other and this three and that
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three councils out, so we would be left with
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three X plus five raise to the negative second power
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. And this is exactly what we were trying to
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integrate. So this is so that formula up there
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does hold.