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Popular >

derivative of (7x)^x

Solution

derivative of

(7 x)^{x}

Solution

(ln (7 x) + 1) (7 x)^{x}

Solution steps

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

Apply exponent rule:

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

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

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

Apply the chain rule:

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

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

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

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

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

= (ln (7 x) + 1) (7 x)^{x}

Popular Examples

integral of (2x+5)/(x^2+x)

\int \frac{2 x + 5}{x ^{2} + x} d x

integral of ((1-2/3 x^2)^6)(x)

\int ((1 - \frac{2}{3} x^{2})^{6}) (x) d x

(\partial)/(\partial y)(sqrt(x^2+y^2-1))

\frac{\partial}{\partial y} (x^{2} + y^{2} - 1)

derivative of (x^2-5x+1(2x+3))

\frac{d}{d x} ((x^{2} - 5 x + 1) (2 x + 3))

(\partial)/(\partial y)(((ax+by))/(cx+dy))

\frac{\partial}{\partial y} (\frac{( a x + b y )}{c x + d y})

Frequently Asked Questions (FAQ)

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