3. How do you differentiate 2x+1 from y=2x+1 how about 9y-8 and 9y-8=4x
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3. How do you differentiate 2x+1 from y=2x+1 how about 9y-8 and 9y-8=4x
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Answer:
1. To differentiate 2x+1, we apply the power rule. We raise y to the power of 1, which gives us 1. Then, we multiply the exponent by the coefficient of the variable we want to differentiate, which in this case is 2. This gives us:
d/Dx [2x + 1] = 2
The resulting equation gives us the gradient of the tangent to the curve at any point.
2. To differentiate 9y - 8, we apply the power rule. We raise y to the power of -1, which gives us -1. Then, we multiply the exponent by the coefficient of the variable we want to differentiate, which in this case is 9. This gives us:
d/Dx [9y - 8] = -9
This equation gives us the gradient of the tangent to the curve at any point.
3. We can rewrite 9y - 8 = 4x as:
9y - 4x - 8 = 0
We differentiate this equation with respect to y, using the implicit differentiation rule:
d/dx (9y - 4x - 8) = 0
d/dx (9) * d/dx (y) - d/dx (4) * d/dx (x) = 0
0 * 9 - 9 * 4 = 0
-36 = 0
This result is not true, so the equation 9y - 8 = 4x does not represent a function of x. Therefore, there is no gradient at any point.
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