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

The derivative of y=x(x^3+3)^5 is (x^3+3)^5+15x^3(x^3+3)^4

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

The first derivative of y=x(x^3+3)^5 is (x^3+3)^5+15x^3(x^3+3)^4

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derivative of

y = x (x^{3} + 3)^{5}

(x^{3} + 3)^{5} + 15 x^{3} (x^{3} + 3)^{4}

Solution steps

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

Apply the Product Rule:

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

f = x, g = (x^{3} + 3)^{5}

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

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

\frac{d}{d x} ((x^{3} + 3)^{5}) = 15 x^{2} (x^{3} + 3)^{4}

= 1 \cdot (x^{3} + 3)^{5} + 15 x^{2} (x^{3} + 3)^{4} x

Simplify

1 \cdot (x^{3} + 3)^{5} + 15 x^{2} (x^{3} + 3)^{4} x : (x^{3} + 3)^{5} + 15 x^{3} (x^{3} + 3)^{4}

= (x^{3} + 3)^{5} + 15 x^{3} (x^{3} + 3)^{4}

f (4 x^{2} - 2)

f (x) = ln (x^{2} - 9)

sin^{2} (+ t)

\frac{d}{d x} (- x)

\frac{\partial}{\partial x} (e^{x y} ln (z))

What is the derivative of y=x(x^3+3)^5 ?
The derivative of y=x(x^3+3)^5 is (x^3+3)^5+15x^3(x^3+3)^4
What is the first derivative of y=x(x^3+3)^5 ?
The first derivative of y=x(x^3+3)^5 is (x^3+3)^5+15x^3(x^3+3)^4