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Popular >

derivative of 2^x(x^2+1)

Solution

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

Solution

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

Popular Examples

(2x-1)dx+(3y+5)dy=0

(2 x - 1) d x + (3 y + 5) d y = 0

integral of (1+4x)^{3/5}

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

(\partial)/(\partial x)(xsin(z))

\frac{\partial}{\partial x} (x sin (z))

x^2y^'+2xy=e^{3x}

x^{2} y^{^{'}} + 2 x y = e^{3 x}

integral from 1 to 3 of (x^2+4)/x

\int_{1}^{3} \frac{x ^{2} + 4}{x} d x

Frequently Asked Questions (FAQ)

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