Question #177626

Differentiate with respect to the variable 


y=x3 - x2 + x + 5. dy/dx


y=x3 + 7x2 - 4x + 8 dy/dx


s=17t3 - 5t2 - 5t - 3 ds/dt




1
Expert's answer
2021-04-15T07:21:27-0400

Solution:

(a):

y=x3x2+x+5y=x^3 - x^2 + x + 5

On differentiating both sides w.r.t xx ,

dydx=3x22x+1+0\frac{dy}{dx}=3x^2-2x+1+0 [Using ddx(xn)=n.xn1\frac{d}{dx}(x^n)=n.x^{n-1} ]

dydx=3x22x+1\Rightarrow \frac{dy}{dx}=3x^2-2x+1

(b):

y=x3+7x24x+8y=x^3 + 7x^2 - 4x + 8

On differentiating both sides w.r.t xx ,

dydx=3x2+7(2)x4(1)+0dydx=3x2+14x4\frac{dy}{dx}=3x^2+7(2)x-4(1)+0 \\\Rightarrow \frac{dy}{dx}=3x^2+14x-4 [Using ddx(xn)=n.xn1\frac{d}{dx}(x^n)=n.x^{n-1} ]

(c):

s=17t35t25t3s=17t^3 - 5t^2 - 5t - 3

On differentiating both sides w.r.t tt ,

dsdt=17(3)t25(2)t5(1)0\frac{ds}{dt}=17(3)t^2-5(2)t-5(1)-0 [Using ddx(xn)=n.xn1\frac{d}{dx}(x^n)=n.x^{n-1} ]

dsdt=51t210t5\Rightarrow \frac{ds}{dt}=51t^2-10t-5


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