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rahulk1
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1. find the differential coefficient of root 2 sin x + 4x power5 -3/x power 4
2. if y=(3x square +1)(x square + 2x) find dy/dx.
2. if y=(3x square +1)(x square + 2x) find dy/dx.
Huh? Is this supposed to be \(\displaystyle \sqrt{2}~sin(x) + 4 x^5 - \frac{3}{x^4}\)rahulk said:1. find the differential coefficient of root 2 sin x + 4x power5 -3/x power 4
Yes it is true kindly slove the problemtopsquark said:Huh? Is this supposed to be \(\displaystyle \sqrt{2}~sin(x) + 4 x^5 - \frac{3}{x^4}\)
-Dan
rahulk said:Yes it is true kindly slove the problem
The differential coefficient of an equation is the rate of change of the equation with respect to its variable. In the given equation, the differential coefficient is the derivative of the equation with respect to x.
To find the differential coefficient of a trigonometric function, you need to use the chain rule. In the given equation, you would first find the derivative of sin x, which is cos x. Then, you would multiply it by the derivative of the inside function, which is 2. This would result in a differential coefficient of 2cos x.
The process for finding the differential coefficient of a polynomial is to first use the power rule to find the derivative of each term. Then, you would add the derivatives together to get the overall differential coefficient. In the given equation, the differential coefficient of 4x^5 would be 20x^4 and the differential coefficient of -3/x^4 would be 12/x^5. Therefore, the overall differential coefficient would be 20x^4 + 12/x^5.
Yes, the differential coefficient can be simplified for this equation. In this case, you would need to combine like terms and use algebraic manipulation to simplify the final result.
Finding the differential coefficient is important in understanding the rate of change of a function and its behavior. It is also a crucial tool in solving optimization problems and determining the slope of a curve at a specific point.