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Popular >

derivative of (7^{10x+1})

Solution

\frac{d}{d x} ((7)^{10 x + 1})

Solution

10 ln (7) \cdot 7^{10 x + 1}

Solution steps

\frac{d}{d x} ((7)^{10 x + 1})

Apply exponent rule:

a^{b} = e^{b l n (a)}

7^{10 x + 1} = e^{(10 x + 1) l n (7)}

= \frac{d}{d x} (e^{(10 x + 1) l n (7)})

Apply the chain rule:

e^{(10 x + 1) l n (7)} \frac{d}{d x} ((10 x + 1) ln (7))

= e^{(10 x + 1) l n (7)} \frac{d}{d x} ((10 x + 1) ln (7))

\frac{d}{d x} ((10 x + 1) ln (7)) = 10 ln (7)

= e^{(10 x + 1) l n (7)} \cdot 10 ln (7)

e^{(10 x + 1) l n (7)} = 7^{10 x + 1}

= 10 ln (7) \cdot 7^{10 x + 1}

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\int_{0}^{\frac{π}{8}} cos^{4} (x) d x

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\frac{d}{d x} (x^{2} \cdot x^{- 1})

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\int \frac{2 x + 1}{x ^{2} + 2 x + 37} d x

(\partial)/(\partial z)(x^2yz)

\frac{\partial}{\partial z} (x^{2} yz)

Frequently Asked Questions (FAQ)

What is the derivative of (7^{10x+1}) ?
The derivative of (7^{10x+1}) is 10ln(7)*7^{10x+1}
What is the first derivative of (7^{10x+1}) ?
The first derivative of (7^{10x+1}) is 10ln(7)*7^{10x+1}