What is the derivative of x(x^6+6) ?

The derivative of x(x^6+6) is 7x^6+6

What is the first derivative of x(x^6+6) ?

The first derivative of x(x^6+6) is 7x^6+6

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derivative of

x (x^{6} + 6)

7 x^{6} + 6

Solution steps

\frac{d}{d x} (x (x^{6} + 6))

Apply the Product Rule:

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

f = x, g = x^{6} + 6

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

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

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

= 1 \cdot (x^{6} + 6) + 6 x^{5} x

Simplify

1 \cdot (x^{6} + 6) + 6 x^{5} x : 7 x^{6} + 6

= 7 x^{6} + 6

\frac{\partial}{\partial x} (y^{3} cos (6 x))

y^{^{''}} - y^{^{'}} = sin (x)

\int_{1}^{3} 2 x d x

\int 2 x y^{3} d x

\int x^{2} cos (3 x) d x

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