What is the derivative of 6x^4(7-6x)^3 ?

The derivative of 6x^4(7-6x)^3 is 6(4x^3(7-6x)^3-18x^4(7-6x)^2)

What is the first derivative of 6x^4(7-6x)^3 ?

The first derivative of 6x^4(7-6x)^3 is 6(4x^3(7-6x)^3-18x^4(7-6x)^2)

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derivative of

6 x^{4} (7 - 6 x)^{3}

6 (4 x^{3} (7 - 6 x)^{3} - 18 x^{4} (7 - 6 x)^{2})

Solution steps

\frac{d}{d x} (6 x^{4} (7 - 6 x)^{3})

Take the constant out:

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

= 6 \frac{d}{d x} (x^{4} (7 - 6 x)^{3})

Apply the Product Rule:

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

f = x^{4}, g = (7 - 6 x)^{3}

= 6 (\frac{d}{d x} (x^{4}) (7 - 6 x)^{3} + \frac{d}{d x} ((7 - 6 x)^{3}) x^{4})

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

\frac{d}{d x} ((7 - 6 x)^{3}) = - 18 (7 - 6 x)^{2}

= 6 (4 x^{3} (7 - 6 x)^{3} + (- 18 (7 - 6 x)^{2}) x^{4})

Simplify

= 6 (4 x^{3} (7 - 6 x)^{3} - 18 x^{4} (7 - 6 x)^{2})

\frac{\partial}{\partial y} (sin^{4} (1 - 4 x y + y^{2}))

f (x) = 500 - y - \frac{4 y}{y + 3}

\int \frac{1}{4 x ^{2} + 5} d x

x \to 0 lim (cos (π) x)

\int 3 x^{- \frac{2}{3}} d x

What is the derivative of 6x^4(7-6x)^3 ?
The derivative of 6x^4(7-6x)^3 is 6(4x^3(7-6x)^3-18x^4(7-6x)^2)
What is the first derivative of 6x^4(7-6x)^3 ?
The first derivative of 6x^4(7-6x)^3 is 6(4x^3(7-6x)^3-18x^4(7-6x)^2)