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Popular >

derivative of (sqrt(x)^{7x})

Solution

\frac{d}{d x} ((x)^{7 x})

Solution

7 x^{\frac{7 x}{2}} (\frac{1}{2} ln (x) + \frac{1}{2})

Solution steps

\frac{d}{d x} ((x)^{7 x})

Apply exponent rule:

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

(x)^{7 x} = e^{7 x l n (x)}

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

Apply the chain rule:

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

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

\frac{d}{d x} (7 x ln (x)) = 7 (ln (x) + \frac{1}{2})

= e^{7 x l n (x)} \cdot 7 (ln (x) + \frac{1}{2})

Simplify

e^{7 x l n (x)} \cdot 7 (ln (x) + \frac{1}{2}) : 7 x^{\frac{7 x}{2}} (\frac{1}{2} ln (x) + \frac{1}{2})

= 7 x^{\frac{7 x}{2}} (\frac{1}{2} ln (x) + \frac{1}{2})

Graph

Popular Examples

integral of (6e^{2x})/(3-e^{4x)}

\int \frac{6 e ^{2 x}}{3 - e ^{4 x}} d x

derivative of 4/(x^4)derivative of

\frac{4}{x ^{4}}

(\partial)/(\partial x)((5x+6y)-(x^2-4xy+8y^2+7x-14y-6))

\frac{\partial}{\partial x} ((5 x + 6 y) - (x^{2} - 4 x y + 8 y^{2} + 7 x - 14 y - 6))

integral from-1 to 3 of sqrt(1+4x^2)

\int_{- 1}^{3} 1 + 4 x^{2} d x

integral of (8t-7)/(t+1)

\int \frac{8 t - 7}{t + 1} d t

Frequently Asked Questions (FAQ)

What is the derivative of (sqrt(x)^{7x}) ?
The derivative of (sqrt(x)^{7x}) is 7x^{(7x)/2}(1/2 ln(x)+1/2)
What is the first derivative of (sqrt(x)^{7x}) ?
The first derivative of (sqrt(x)^{7x}) is 7x^{(7x)/2}(1/2 ln(x)+1/2)