Question

Diffentiation of y=(5x -2)^3
Po

Answer 1

Given:

Function $\bf\:y=\sf\:(5x-2){}^{3}$

To Find :

$\dfrac{dy}{dx}$

Formulas :

$1) \: \frac{d(x {}^{n} )}{dx} = nx {}^{n - 1}$

$2) \frac{d(constant)}{dx} = 0$

$3) \frac{d(sinx)}{dx} = cosx$

$4) \frac{d(cosx)}{dx} = -sinx$

Solution :

$y = (5x - 2) {}^{3}$

Now Differentiate with respect to x

$\bf \frac{dy}{dx} = \frac{d(5x - 2) {}^{3} }{d(5x - 2)} \times \frac{d(5x - 2)}{dx}$

$\sf \frac{dy}{dx} = 3(5x - 2) {}^{2} \times 5$

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More About Differention:

1) A function is said to be differentiable at a point, if there exists a unique tangent at that point .

2)Every polynomial function is differentiable at each x∈R .