What is the derivative of f(x)=72x(6x^2+8)^5 ?

The derivative of f(x)=72x(6x^2+8)^5 is 72((6x^2+8)^5+60x^2(6x^2+8)^4)

What is the first derivative of f(x)=72x(6x^2+8)^5 ?

The first derivative of f(x)=72x(6x^2+8)^5 is 72((6x^2+8)^5+60x^2(6x^2+8)^4)

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derivative of

f (x) = 72 x (6 x^{2} + 8)^{5}

72 ((6 x^{2} + 8)^{5} + 60 x^{2} (6 x^{2} + 8)^{4})

Solution steps

\frac{d}{d x} (72 x (6 x^{2} + 8)^{5})

Take the constant out:

(a \cdot f)^{'} = a \cdot f^{'}

= 72 \frac{d}{d x} (x (6 x^{2} + 8)^{5})

Apply the Product Rule:

(f \cdot g)^{'} = f^{'} \cdot g + f \cdot g^{'}

f = x, g = (6 x^{2} + 8)^{5}

= 72 (\frac{d x}{d x} (6 x^{2} + 8)^{5} + \frac{d}{d x} ((6 x^{2} + 8)^{5}) x)

\frac{d x}{d x} = 1

\frac{d}{d x} ((6 x^{2} + 8)^{5}) = 60 x (6 x^{2} + 8)^{4}

= 72 (1 \cdot (6 x^{2} + 8)^{5} + 60 x (6 x^{2} + 8)^{4} x)

Simplify

72 (1 \cdot (6 x^{2} + 8)^{5} + 60 x (6 x^{2} + 8)^{4} x) : 72 ((6 x^{2} + 8)^{5} + 60 x^{2} (6 x^{2} + 8)^{4})

= 72 ((6 x^{2} + 8)^{5} + 60 x^{2} (6 x^{2} + 8)^{4})

\frac{\partial}{\partial x} (1 + x)

\int_{- 5}^{5} 10 d x

tan^{2} (7 x)

\int_{0}^{\frac{π}{2}} 5 sec^{4} (\frac{t}{2}) d t

\int \frac{- 1200 x}{25 - x ^{2}} d x

What is the derivative of f(x)=72x(6x^2+8)^5 ?
The derivative of f(x)=72x(6x^2+8)^5 is 72((6x^2+8)^5+60x^2(6x^2+8)^4)
What is the first derivative of f(x)=72x(6x^2+8)^5 ?
The first derivative of f(x)=72x(6x^2+8)^5 is 72((6x^2+8)^5+60x^2(6x^2+8)^4)