What is the derivative of 7^{x^4+x} ?

The derivative of 7^{x^4+x} is ln(7)*7^{x^4+x}(4x^3+1)

What is the first derivative of 7^{x^4+x} ?

The first derivative of 7^{x^4+x} is ln(7)*7^{x^4+x}(4x^3+1)

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derivative of

7^{x^{4} + x}

ln (7) \cdot 7^{x^{4} + x} (4 x^{3} + 1)

Solution steps

\frac{d}{d x} (7^{x^{4} + x})

Apply exponent rule:

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

7^{x^{4} + x} = e^{(x^{4} + x) l n (7)}

= \frac{d}{d x} (e^{(x^{4} + x) l n (7)})

Apply the chain rule:

e^{(x^{4} + x) l n (7)} \frac{d}{d x} ((x^{4} + x) ln (7))

= e^{(x^{4} + x) l n (7)} \frac{d}{d x} ((x^{4} + x) ln (7))

\frac{d}{d x} ((x^{4} + x) ln (7)) = ln (7) (4 x^{3} + 1)

= e^{(x^{4} + x) l n (7)} ln (7) (4 x^{3} + 1)

e^{(x^{4} + x) l n (7)} = 7^{x^{4} + x}

= ln (7) \cdot 7^{x^{4} + x} (4 x^{3} + 1)

\int (sin (t) 1 + cos (t)) d t

y = 3 x - 2 x, (1, 1)

(2 e^{y} - x) \frac{d y}{d x} = 1

\frac{d}{d x} ((7 + x)^{5})

x \to - 0 lim (ln (x))

What is the derivative of 7^{x^4+x} ?
The derivative of 7^{x^4+x} is ln(7)*7^{x^4+x}(4x^3+1)
What is the first derivative of 7^{x^4+x} ?
The first derivative of 7^{x^4+x} is ln(7)*7^{x^4+x}(4x^3+1)