en

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

derivative of x(3x+1^5)

Solution

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

Solution

(3 x + 1)^{5} + 15 x (3 x + 1)^{4}

Solution steps

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

Apply the Product Rule:

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

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

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

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

\frac{d}{d x} ((3 x + 1)^{5}) = 15 (3 x + 1)^{4}

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

Simplify

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

Popular Examples

limit as x approaches 1 of (sin(x-1))/x

x \to 1 lim (\frac{sin ( x - 1 )}{x})

integral of (ln(2x))/(3x)

\int \frac{ln ( 2 x )}{3 x} d x

tangent of f(x)=3sin(x),\at x=-pi/4 tangent of

f (x) = 3 sin (x), at x = - \frac{π}{4}

derivative of y=80(1-e^{-0.041x})derivative of

y = 80 (1 - e^{- 0.041 x})

(\partial)/(\partial x)(y(x^2+y)^6)

\frac{\partial}{\partial x} (y (x^{2} + y)^{6})

Frequently Asked Questions (FAQ)

What is the derivative of x(3x+1^5) ?
The derivative of x(3x+1^5) is (3x+1)^5+15x(3x+1)^4
What is the first derivative of x(3x+1^5) ?
The first derivative of x(3x+1^5) is (3x+1)^5+15x(3x+1)^4