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

The derivative of 2^x(x^2+1) is ln(2)*2^x(x^2+1)+2^{1+x}x

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

The first derivative of 2^x(x^2+1) is ln(2)*2^x(x^2+1)+2^{1+x}x

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

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

ln (2) \cdot 2^{x} (x^{2} + 1) + 2^{1 + x} x

Solution steps

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

Apply the Product Rule:

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

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

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

\frac{d}{d x} (2^{x}) = 2^{x} ln (2)

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

= 2^{x} ln (2) (x^{2} + 1) + 2 x \cdot 2^{x}

Apply exponent rule:

a^{b} \cdot a^{c} = a^{b + c}

2 \cdot 2^{x} = 2^{1 + x}

= ln (2) \cdot 2^{x} (x^{2} + 1) + 2^{1 + x} x

What is the derivative of 2^x(x^2+1) ?
The derivative of 2^x(x^2+1) is ln(2)*2^x(x^2+1)+2^{1+x}x
What is the first derivative of 2^x(x^2+1) ?
The first derivative of 2^x(x^2+1) is ln(2)*2^x(x^2+1)+2^{1+x}x