What is the derivative of f(x)=6x^6(x^4-6x) ?

The derivative of f(x)=6x^6(x^4-6x) is 6(10x^9-42x^6)

What is the first derivative of f(x)=6x^6(x^4-6x) ?

The first derivative of f(x)=6x^6(x^4-6x) is 6(10x^9-42x^6)

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derivative of

f (x) = 6 x^{6} (x^{4} - 6 x)

6 (10 x^{9} - 42 x^{6})

Solution steps

\frac{d}{d x} (6 x^{6} (x^{4} - 6 x))

Take the constant out:

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

= 6 \frac{d}{d x} (x^{6} (x^{4} - 6 x))

Apply the Product Rule:

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

f = x^{6}, g = x^{4} - 6 x

= 6 (\frac{d}{d x} (x^{6}) (x^{4} - 6 x) + \frac{d}{d x} (x^{4} - 6 x) x^{6})

\frac{d}{d x} (x^{6}) = 6 x^{5}

\frac{d}{d x} (x^{4} - 6 x) = 4 x^{3} - 6

= 6 (6 x^{5} (x^{4} - 6 x) + (4 x^{3} - 6) x^{6})

Expand

6 x^{5} (x^{4} - 6 x) + (4 x^{3} - 6) x^{6} : 10 x^{9} - 42 x^{6}

= 6 (10 x^{9} - 42 x^{6})

f (x) = e^{x}, at x = ln (3)

\int \frac{x ^{3}}{x ^{2} + 4} d x

5 sin (3 t - \frac{π}{4})

e^{x}, e^{- x}, [0, 1]

\frac{\partial}{\partial x} ((x^{3} - y^{2})^{- 1})

What is the derivative of f(x)=6x^6(x^4-6x) ?
The derivative of f(x)=6x^6(x^4-6x) is 6(10x^9-42x^6)
What is the first derivative of f(x)=6x^6(x^4-6x) ?
The first derivative of f(x)=6x^6(x^4-6x) is 6(10x^9-42x^6)