What is the derivative of (10x+2^x) ?

The derivative of (10x+2^x) is (ln(10x+2)+(5x)/(5x+1))(10x+2)^x

What is the first derivative of (10x+2^x) ?

The first derivative of (10x+2^x) is (ln(10x+2)+(5x)/(5x+1))(10x+2)^x

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\frac{d}{d x} ((10 x + 2)^{x})

(ln (10 x + 2) + \frac{5 x}{5 x + 1}) (10 x + 2)^{x}

Solution steps

\frac{d}{d x} ((10 x + 2)^{x})

Apply exponent rule:

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

(10 x + 2)^{x} = e^{x l n (10 x + 2)}

= \frac{d}{d x} (e^{x l n (10 x + 2)})

Apply the chain rule:

e^{x l n (10 x + 2)} \frac{d}{d x} (x ln (10 x + 2))

= e^{x l n (10 x + 2)} \frac{d}{d x} (x ln (10 x + 2))

\frac{d}{d x} (x ln (10 x + 2)) = ln (10 x + 2) + \frac{5 x}{5 x + 1}

= e^{x l n (10 x + 2)} (ln (10 x + 2) + \frac{5 x}{5 x + 1})

e^{x l n (10 x + 2)} = (10 x + 2)^{x}

= (ln (10 x + 2) + \frac{5 x}{5 x + 1}) (10 x + 2)^{x}

x y^{3}

\frac{d y}{d x}, y = x + \frac{1}{x}

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

n = 0 \sum \infty 6 (\frac{4}{5})^{n}

\int \frac{tan ( ln ( 4 x + 2 ) )}{4 x + 2} d x

What is the derivative of (10x+2^x) ?
The derivative of (10x+2^x) is (ln(10x+2)+(5x)/(5x+1))(10x+2)^x
What is the first derivative of (10x+2^x) ?
The first derivative of (10x+2^x) is (ln(10x+2)+(5x)/(5x+1))(10x+2)^x