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Popular >

derivative of 5^x(x^2+1)

Solution

derivative of

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

Solution

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}

Popular Examples

derivative of 4x^2+2x+1n(x-3x^2-7x-3)

\frac{d}{d x} (4 x^{2} + 2 x + 1 n (x) - 3 x^{2} - 7 x - 3)

derivative of y=4x^3(2-3x)derivative of

y = 4 x^{3} (2 - 3 x)

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(x + 6)^{5}

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y = \frac{t ^{3}}{3}

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Frequently Asked Questions (FAQ)

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