What is the derivative of x(x^4+5^5) ?

The derivative of x(x^4+5^5) is (x^4+5)^5+20x^4(x^4+5)^4

What is the first derivative of x(x^4+5^5) ?

The first derivative of x(x^4+5^5) is (x^4+5)^5+20x^4(x^4+5)^4

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\frac{d}{d x} (x (x^{4} + 5)^{5})

(x^{4} + 5)^{5} + 20 x^{4} (x^{4} + 5)^{4}

Solution steps

\frac{d}{d x} (x (x^{4} + 5)^{5})

Apply the Product Rule:

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

f = x, g = (x^{4} + 5)^{5}

= \frac{d x}{d x} (x^{4} + 5)^{5} + \frac{d}{d x} ((x^{4} + 5)^{5}) x

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

\frac{d}{d x} ((x^{4} + 5)^{5}) = 20 x^{3} (x^{4} + 5)^{4}

= 1 \cdot (x^{4} + 5)^{5} + 20 x^{3} (x^{4} + 5)^{4} x

Simplify

1 \cdot (x^{4} + 5)^{5} + 20 x^{3} (x^{4} + 5)^{4} x : (x^{4} + 5)^{5} + 20 x^{4} (x^{4} + 5)^{4}

= (x^{4} + 5)^{5} + 20 x^{4} (x^{4} + 5)^{4}

\int_{0}^{\infty} a e^{- a x} d x

n = 0 \sum \infty ln (n)

n = 0 \sum \infty \frac{3}{1 0 ^{n}}

x^{2} y^{^{''}} - 4 x y^{^{'}} + 4 y = 0

\int (cos^{3} (x) \cdot sin^{- 4} (x)) d x

What is the derivative of x(x^4+5^5) ?
The derivative of x(x^4+5^5) is (x^4+5)^5+20x^4(x^4+5)^4
What is the first derivative of x(x^4+5^5) ?
The first derivative of x(x^4+5^5) is (x^4+5)^5+20x^4(x^4+5)^4