What is the derivative of (a^x^3+x^2+x) ?

The derivative of (a^x^3+x^2+x) is 3a^{3x}ln(a)+2x+1

What is the first derivative of (a^x^3+x^2+x) ?

The first derivative of (a^x^3+x^2+x) is 3a^{3x}ln(a)+2x+1

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\frac{d}{d x} ((a^{x})^{3} + x^{2} + x)

3 a^{3 x} ln (a) + 2 x + 1

Solution steps

\frac{d}{d x} ((a^{x})^{3} + x^{2} + x)

Simplify

(a^{x})^{3} + x^{2} + x : a^{3 x} + x^{2} + x

= \frac{d}{d x} (a^{3 x} + x^{2} + x)

Apply the Sum/Difference Rule:

(f \pm g)^{'} = f^{'} \pm g^{'}

= \frac{d}{d x} (a^{3 x}) + \frac{d}{d x} (x^{2}) + \frac{d x}{d x}

\frac{d}{d x} (a^{3 x}) = 3 a^{3 x} ln (a)

\frac{d}{d x} (x^{2}) = 2 x

\frac{d x}{d x} = 1

= 3 a^{3 x} ln (a) + 2 x + 1

What is the derivative of (a^x^3+x^2+x) ?
The derivative of (a^x^3+x^2+x) is 3a^{3x}ln(a)+2x+1
What is the first derivative of (a^x^3+x^2+x) ?
The first derivative of (a^x^3+x^2+x) is 3a^{3x}ln(a)+2x+1