Example Solutions for

Step-by-Step Derivatives

Derivatives

Analyze derivatives step by step.

Explore the steps for derivative calculations using the power rule:

d/dx sqrt(x)
derivative of 1/x^2

Find the derivative using the product rule:

compute the derivative of x*sin[x]
f'(x) if f(x) = (x+1)(x^2 + 3)

Compute derivatives using the quotient rule:

d/dx of (x^2-x)/(x^2+3)
slope of log(t) / (t^2 + 1)

See step by step how to apply the chain rule:

derivative of exp(sin(x))
derivative of (cos(log(x)))^3

Use the limit definition to compute derivatives:

d/dz of sin(z)
find d/dx for (x^2)/x^3

Find partial derivatives of multivariate expressions:

partial derivatives of exp(-x^2 - y^2)
partial derivative of cos( 3 pi /4 * x + 5 pi /3 * y + pi / 2 * z) with respect to y

See how to evaluate derivatives at a given point:

derivative of x^2+4x-2 at x=3
d/dt arctan(t) at t = 1

Perform logarithmic differentiation to compute a derivative:

first derivative of 1/x^3
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