What is the derivative of (3x^2+x)(5x^3+1) ?

The derivative of (3x^2+x)(5x^3+1) is 75x^4+20x^3+6x+1

What is the first derivative of (3x^2+x)(5x^3+1) ?

The first derivative of (3x^2+x)(5x^3+1) is 75x^4+20x^3+6x+1

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derivative of

(3 x^{2} + x) (5 x^{3} + 1)

75 x^{4} + 20 x^{3} + 6 x + 1

Solution steps

\frac{d}{d x} ((3 x^{2} + x) (5 x^{3} + 1))

Apply the Product Rule:

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

f = 3 x^{2} + x, g = 5 x^{3} + 1

= \frac{d}{d x} (3 x^{2} + x) (5 x^{3} + 1) + \frac{d}{d x} (5 x^{3} + 1) (3 x^{2} + x)

\frac{d}{d x} (3 x^{2} + x) = 6 x + 1

\frac{d}{d x} (5 x^{3} + 1) = 15 x^{2}

= (6 x + 1) (5 x^{3} + 1) + 15 x^{2} (3 x^{2} + x)

Simplify

(6 x + 1) (5 x^{3} + 1) + 15 x^{2} (3 x^{2} + x) : 75 x^{4} + 20 x^{3} + 6 x + 1

= 75 x^{4} + 20 x^{3} + 6 x + 1

\int \frac{- 1}{e ^{x}} d x

\int x (x^{4} + \frac{1}{4} x) d x

\int y^{3} e^{y^{4}} d y

\frac{d}{d x} (cos ((π x)^{9}))

\frac{\partial}{\partial x} (x^{0.1})

What is the derivative of (3x^2+x)(5x^3+1) ?
The derivative of (3x^2+x)(5x^3+1) is 75x^4+20x^3+6x+1
What is the first derivative of (3x^2+x)(5x^3+1) ?
The first derivative of (3x^2+x)(5x^3+1) is 75x^4+20x^3+6x+1