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Popular >

derivative of x5^{6x+1}

Solution

derivative of

x 5^{6 x + 1}

Solution

5^{6 x + 1} + 6 ln (5) \cdot 5^{6 x + 1} x

Solution steps

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

Apply the Product Rule:

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

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

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

\frac{d x}{d x} = 1

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

= 1 \cdot 5^{6 x + 1} + 6 ln (5) \cdot 5^{6 x + 1} x

Simplify

= 5^{6 x + 1} + 6 ln (5) \cdot 5^{6 x + 1} x

Popular Examples

derivative of f(x)=(x^2-1)/(x+3)derivative of

f (x) = \frac{x ^{2} - 1}{x + 3}

(\partial)/(\partial x)(6xy+e^xln(y)-5)

\frac{\partial}{\partial x} (6 x y + e^{x} ln (y) - 5)

integral from 0 to 1 of ln(1-x)

\int_{0}^{1} ln (1 - x) d x

integral from 0 to pi/(20) of tan(10x)

\int_{0}^{\frac{π}{20}} tan (10 x) d x

derivative of (x+4/(cos(x)))

\frac{d}{d x} (\frac{x + 4}{cos ( x )})

Frequently Asked Questions (FAQ)

What is the derivative of x5^{6x+1} ?
The derivative of x5^{6x+1} is 5^{6x+1}+6ln(5)*5^{6x+1}x
What is the first derivative of x5^{6x+1} ?
The first derivative of x5^{6x+1} is 5^{6x+1}+6ln(5)*5^{6x+1}x