What is the derivative of 7^{x+arccos(x)} ?

The derivative of 7^{x+arccos(x)} is ln(7)*7^{x+arccos(x)}(1-1/(sqrt(1-x^2)))

What is the first derivative of 7^{x+arccos(x)} ?

The first derivative of 7^{x+arccos(x)} is ln(7)*7^{x+arccos(x)}(1-1/(sqrt(1-x^2)))

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derivative of

7^{x + a r c c o s (x)}

ln (7) \cdot 7^{x + a r c c o s (x)} (1 - \frac{1}{1 - x ^{2}})

Solution steps

\frac{d}{d x} (7^{x + a r c c o s (x)})

Apply exponent rule:

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

7^{x + a r c c o s (x)} = e^{(x + a r c c o s (x)) l n (7)}

= \frac{d}{d x} (e^{(x + a r c c o s (x)) l n (7)})

Apply the chain rule:

e^{(x + a r c c o s (x)) l n (7)} \frac{d}{d x} ((x + arccos (x)) ln (7))

= e^{(x + a r c c o s (x)) l n (7)} \frac{d}{d x} ((x + arccos (x)) ln (7))

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

= e^{(x + a r c c o s (x)) l n (7)} ln (7) (1 - \frac{1}{1 - x ^{2}})

e^{(x + a r c c o s (x)) l n (7)} = 7^{x + a r c c o s (x)}

= ln (7) \cdot 7^{x + a r c c o s (x)} (1 - \frac{1}{1 - x ^{2}})

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