What is the derivative of 7x^7(7-x^8) ?

The derivative of 7x^7(7-x^8) is 7(7x^6(7-x)^8-8x^7(7-x)^7)

What is the first derivative of 7x^7(7-x^8) ?

The first derivative of 7x^7(7-x^8) is 7(7x^6(7-x)^8-8x^7(7-x)^7)

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\frac{d}{d x} (7 x^{7} (7 - x)^{8})

7 (7 x^{6} (7 - x)^{8} - 8 x^{7} (7 - x)^{7})

Solution steps

\frac{d}{d x} (7 x^{7} (7 - x)^{8})

Take the constant out:

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

= 7 \frac{d}{d x} (x^{7} (7 - x)^{8})

Apply the Product Rule:

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

f = x^{7}, g = (7 - x)^{8}

= 7 (\frac{d}{d x} (x^{7}) (7 - x)^{8} + \frac{d}{d x} ((7 - x)^{8}) x^{7})

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

\frac{d}{d x} ((7 - x)^{8}) = - 8 (7 - x)^{7}

= 7 (7 x^{6} (7 - x)^{8} + (- 8 (7 - x)^{7}) x^{7})

Simplify

= 7 (7 x^{6} (7 - x)^{8} - 8 x^{7} (7 - x)^{7})

x \to \infty lim ((1 + \frac{1}{7 x})^{9 x})

\frac{d}{d x} (- x^{2} + 2 x)

x \to \infty lim (cos (\frac{x π}{x + 1}))

\frac{d x}{d t}

x \to \infty lim (3 x - 2)

What is the derivative of 7x^7(7-x^8) ?
The derivative of 7x^7(7-x^8) is 7(7x^6(7-x)^8-8x^7(7-x)^7)
What is the first derivative of 7x^7(7-x^8) ?
The first derivative of 7x^7(7-x^8) is 7(7x^6(7-x)^8-8x^7(7-x)^7)