What is the derivative of 3x(x^4+5)^5 ?

The derivative of 3x(x^4+5)^5 is 3((x^4+5)^5+20x^4(x^4+5)^4)

What is the first derivative of 3x(x^4+5)^5 ?

The first derivative of 3x(x^4+5)^5 is 3((x^4+5)^5+20x^4(x^4+5)^4)

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derivative of

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

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

Solution steps

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

Take the constant out:

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

= 3 \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}

= 3 (\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}

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

Simplify

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

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

\int cos^{4} (x) \cdot sin^{2} (x) d x

3 sin (x) + 2 cos (x)

\frac{d}{d x} (\frac{π x}{3})

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

\int \frac{2}{3} (x - 1)^{\frac{3}{2}} d x

What is the derivative of 3x(x^4+5)^5 ?
The derivative of 3x(x^4+5)^5 is 3((x^4+5)^5+20x^4(x^4+5)^4)
What is the first derivative of 3x(x^4+5)^5 ?
The first derivative of 3x(x^4+5)^5 is 3((x^4+5)^5+20x^4(x^4+5)^4)