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Popular >

derivative of x^6(5.1)^x

Solution

derivative of

x^{6} (5.1)^{x}

Solution

6 x^{5} \cdot 5. 1^{x} + 1.62924 \dots \cdot 5. 1^{x} x^{6}

Solution steps

\frac{d}{d x} (x^{6} \cdot 5. 1^{x})

Apply the Product Rule:

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

f = x^{6}, g = 5. 1^{x}

= \frac{d}{d x} (x^{6}) 5. 1^{x} + \frac{d}{d x} (5. 1^{x}) x^{6}

\frac{d}{d x} (x^{6}) = 6 x^{5}

\frac{d}{d x} (5. 1^{x}) = 1.62924 \dots \cdot 5. 1^{x}

= 6 x^{5} \cdot 5. 1^{x} + 1.62924 \dots \cdot 5. 1^{x} x^{6}

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Frequently Asked Questions (FAQ)

What is the derivative of x^6(5.1)^x ?
The derivative of x^6(5.1)^x is 6x^5*5.1^x+1.62924…*5.1^xx^6
What is the first derivative of x^6(5.1)^x ?
The first derivative of x^6(5.1)^x is 6x^5*5.1^x+1.62924…*5.1^xx^6