Find the derivative with respect to x . 1. y = (-4x^6) /...

Find the derivative with respect to x . 1. y = (-4x^6) / 5 2. y = 3x^4 e^{2x} 3. y = 8ln(x - 9) 4. y = 6tan(2x) 5. y = x^5 - 3x^7 6. y = 3x^{3/4} 7. y = sqrt(9 - 5x) 8. y = 4sin(7x)

Transcript

00:01 Hello everyone, in this question we have to find the derivative with respect to x.

00:04 The first part is y equal to minus 4x to the power 6 by 5.

00:08 So y dash will be minus 4 by 5 d by dx of x to the power 6 will be minus 4 by 5 6x to the power 5 that is minus 24 by 5 x to the power 5.

00:21 Then the second part is y equal to 3x to the power 4 e to the power 2x.

00:26 So y dash will be taking 3 common we will be having d by dx of x to the power 4 e to the power 2x.

00:34 So this is nothing but uv method.

00:36 So first keep x4 as it is differentiating this we will be having 2 e to the power 2x then keeping e to the power 2x and differentiating x4 we will be having 4x cube.

00:47 So 3 2's are 6 x to the power 4 e to the power 2x then 4 3's are 12 12 x cube e to the power 2x.

00:55 This is the final then third one is the third part is y equal to 8 log of x minus 9.

01:06 So y dash will be taking 8 common d by dx of log of x minus 9 is nothing but 1 of x minus 9 then again differentiating d by dx of x minus 9.

01:19 So 8 1 by x minus 9 differentiating we will be having 1 minus 0.

01:26 So 8 1 by x minus 9 that is 8 divided by x minus 9 and the fourth part is y equal to 6 tan 2x then y dash will be 6 into d by dx of tan 2x.

01:45 So the differentiation of tan x is nothing but 6 secant square 2x again differentiating 2x will be having 2...

Question

Find the derivative with respect to x . 1. y = (-4x^6) / 5 2. y = 3x^4 e^{2x} 3. y = 8ln(x - 9) 4. y = 6tan(2x) 5. y = x^5 - 3x^7 6. y = 3x^{3/4} 7. y = sqrt(9 - 5x) 8. y = 4sin(7x)

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