Answer to Question #177626 in Differential Geometry | Topology for John

Question

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

Answer 1

Solution:

(a):

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

On differentiating both sides w.r.t $x$ ,

$\frac{dy}{dx}=3x^2-2x+1+0$ [Using $\frac{d}{dx}(x^n)=n.x^{n-1}$ ]

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

(b):

$y=x^3 + 7x^2 - 4x + 8$

On differentiating both sides w.r.t $x$ ,

$\frac{dy}{dx}=3x^2+7(2)x-4(1)+0 \\\Rightarrow \frac{dy}{dx}=3x^2+14x-4$ [Using $\frac{d}{dx}(x^n)=n.x^{n-1}$ ]

(c):

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

On differentiating both sides w.r.t $t$ ,

$\frac{ds}{dt}=17(3)t^2-5(2)t-5(1)-0$ [Using $\frac{d}{dx}(x^n)=n.x^{n-1}$ ]

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