Question

differentiation of t^3 - 6t^2 - 15t + 40

Answer 1

Answer :

The differentiation of t³ - 6t² - 15t + 40 is 3t² - 12t - 15.

Explanation :

To find :

• The derivative of t³ - 6t² - 15t + 40.

Knowledge required :

• Exponent rule of differentiation :

⠀⠀⠀⠀⠀⠀⠀⠀⠀$\boxed{\sf\dfrac{d(x^{n})}{dx} = nx^{(n - 1)}}$

• Differentiation of a constant term is 0.

⠀⠀⠀⠀⠀⠀⠀⠀⠀$\boxed{\sf{\dfrac{d(c)}{dx} = 0}}$

Solution :

By differentiating the given equation with respect to t, we get :

$:\implies \sf{\dfrac{dy}{dx} = \dfrac{d(t^{3} - 6t^{2} - 15t + 50}{dt}} \\ \\ :\implies \sf{\dfrac{dy}{dx} = \dfrac{d(t^{3}}{dt} - \dfrac{d(6t^{2})}{dt} - \dfrac{d(15t)}{dt} + \dfrac{d(50)}{dt}} \\ \\ :\implies \sf{\dfrac{dy}{dx} = [3 \times t^{(3 - 1)}] - [2 \times 6t^{(2 - 1)} - [1 \times 15t^{(1 - 1)}] + 0} \\ \\ :\implies \sf{\dfrac{dy}{dx} = [3 \times t^{2}] - [2 \times 6t^{1}] - [1 \times 15t^{0}]} \\ \\ :\implies \sf{\dfrac{dy}{dx} = 3t^{2} - 12t - 15} \\ \\ \boxed{\therefore \sf{\dfrac{dy}{dx} = 3t^{2} - 12t - 15}}$

Hence the derivative of t³ - 6t² - 15t + 40 is 3t² - 12t - 15.

Know more!

• chain rule of differentiation :

$\boxed{\sf{\dfrac{d(y)}{dx} = \dfrac{d(y)}{du} \times \dfrac{d(u)}{dx}}}$

• Product rule of differentiation :

$\boxed{\sf{\dfrac{d(vu)}{dx} = u\dfrac{d(v)}{dx} + v\dfrac{d(u)}{dx}}}$

• Quotient rule of differentiation :

$\boxed{\sf{\dfrac{d}{dx}\bigg(\dfrac{v}{u}\bigg) = \dfrac{v\dfrac{d(u)}{dx} + u\dfrac{d(v)}{dx}}{v^{2}}}}$

Answer 2

Answer:

Explanation:

Answer :

The differentiation of t³ - 6t² - 15t + 40 is 3t² - 12t - 15.

Explanation :

To find :

The derivative of t³ - 6t² - 15t + 40.

Knowledge required :

Exponent rule of differentiation :

⠀⠀⠀⠀⠀⠀⠀⠀⠀

Differentiation of a constant term is 0.

⠀⠀⠀⠀⠀⠀⠀⠀⠀

Solution :

By differentiating the given equation with respect to t, we get :

Hence the derivative of t³ - 6t² - 15t + 40 is 3t² - 12t - 15.

Know more!

chain rule of differentiation :

Product rule of differentiation :

Quotient rule of differentiation :

Answer :

The differentiation of t³ - 6t² - 15t + 40 is 3t² - 12t - 15.

Explanation :

To find :

The derivative of t³ - 6t² - 15t + 40.

Knowledge required :

Exponent rule of differentiation :

⠀⠀⠀⠀⠀⠀⠀⠀⠀

Differentiation of a constant term is 0.

⠀⠀⠀⠀⠀⠀⠀⠀⠀

Solution :

By differentiating the given equation with respect to t, we get :

Hence the derivative of t³ - 6t² - 15t + 40 is 3t² - 12t - 15.

Know more!

chain rule of differentiation :

Product rule of differentiation :

Quotient rule of differentiation :