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

The derivative of 5^x(x^2+1) is 5^xln(5)(x^2+1)+2x*5^x

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

The first derivative of 5^x(x^2+1) is 5^xln(5)(x^2+1)+2x*5^x

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derivative of

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

5^{x} ln (5) (x^{2} + 1) + 2 x \cdot 5^{x}

Solution steps

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

Apply the Product Rule:

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

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

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

\frac{d}{d x} (5^{x}) = 5^{x} ln (5)

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

= 5^{x} ln (5) (x^{2} + 1) + 2 x \cdot 5^{x}

What is the derivative of 5^x(x^2+1) ?
The derivative of 5^x(x^2+1) is 5^xln(5)(x^2+1)+2x*5^x
What is the first derivative of 5^x(x^2+1) ?
The first derivative of 5^x(x^2+1) is 5^xln(5)(x^2+1)+2x*5^x