What is the derivative of f(x)=e^{xsqrt(7x+6)} ?

The derivative of f(x)=e^{xsqrt(7x+6)} is (e^{xsqrt(7x+6)}(21x+12))/(2sqrt(7x+6))

What is the first derivative of f(x)=e^{xsqrt(7x+6)} ?

The first derivative of f(x)=e^{xsqrt(7x+6)} is (e^{xsqrt(7x+6)}(21x+12))/(2sqrt(7x+6))

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derivative of

f (x) = e^{x 7 x + 6}

\frac{e ^{x 7 x + 6} ( 21 x + 12 )}{2 7 x + 6}

Solution steps

\frac{d}{d x} (e^{x 7 x + 6})

Apply the chain rule:

e^{x 7 x + 6} \frac{d}{d x} (x 7 x + 6)

= e^{x 7 x + 6} \frac{d}{d x} (x 7 x + 6)

\frac{d}{d x} (x 7 x + 6) = \frac{21 x + 12}{2 7 x + 6}

= e^{x 7 x + 6} \frac{21 x + 12}{2 7 x + 6}

Multiply fractions:

a \cdot \frac{b}{c} = \frac{a \cdot b}{c}

= \frac{e ^{x 7 x + 6} ( 21 x + 12 )}{2 7 x + 6}

What is the derivative of f(x)=e^{xsqrt(7x+6)} ?
The derivative of f(x)=e^{xsqrt(7x+6)} is (e^{xsqrt(7x+6)}(21x+12))/(2sqrt(7x+6))
What is the first derivative of f(x)=e^{xsqrt(7x+6)} ?
The first derivative of f(x)=e^{xsqrt(7x+6)} is (e^{xsqrt(7x+6)}(21x+12))/(2sqrt(7x+6))